Solve the equation a + x - a - x a + x + a - x = x a , a ≠ 0 .

The given equation is a + x - a - x a + x + a - x = x a Applying componendo and dividendo we get, a + x - a - x + a + x + a - x a + x + a - x - a + x + a - x = a + x a - x ∵ p q = r s ⇒ q + p q - p = s + r s - r a + x a - x = a + x a - x Squaring both sides and cross multiplying we get, ( a + x ) ( a - x ) 2 = ( a + x ) 2 ( a - x ) ( a + x ) ( a - x ) ( a + x - a + x ) = 0 ( a 2 - x 2 ) x = 0 So either x = 0 or x 2 - a 2 = 0 which is a quadratic equation whose middle term is missing. So its roots are x = ± 4 a 2 2 ∴ x = ± a , 0 are the required solutions.

Solve the equation x + 1 x 2 - 2 x - 1 x + 4 = 11 .

The given equation is x + 1 x 2 - 2 x - 1 x + 4 = 11 Let us assume x - 1 x = t , squaring both sides we get x 2 + 1 x 2 - 2 = t 2 So the given equation is now, x 2 + 1 x 2 + 2 - 2 t - 8 = 11 t 2 + 2 + 2 - 2 t - 19 = 0 t 2 - 2 t - 15 = 0 is a quadratic equation whose roots are given by, t = 2 ± 64 2 So we get t = 5 or t = - 3 Now x - 1 x = t ⇒ x 2 - t x - 1 = 0 which is a quadratic in x . So x = t ± t 2 + 4 2 Using t = 5 & t = - 3 we get, x = 5 ± 29 2 , - 3 ± 13 2 as the required solutions.

Solve the simultaneous equations x y + y x = 2 1 2 , x + y = 10

The given equations are x y + y x = 2 1 2 , x + y = 10 Let us assume x y = t t > 0 So the first equation is t + 1 t = 5 2 2 t 2 - 5 t + 2 = 0 is a quadratic whose roots are, t = 5 ± 9 4 So we have t = 2 or t = 1 2 x y = 2 or 1 2 x y = 4 or 1 4 If x = 4 y , when we use second equation we get, x + y = 10 ⇒ 5 y = 10 y = 2 so x = 8 . Now if x = y 4 , we get y + y 4 = 10 5 y 4 = 10 ⇒ y = 8 and so x = 2 . Thus the solution set is ( x , y ) = ( 8 , 2 ) or ( 2 , 8 )

E M B I B E

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.2

M L Aggarwal Solutions for Chapter: Quadratic Equations, Exercise 2: EXERCISE 6.2

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Quadratic Equations, Exercise 2: EXERCISE 6.2

Attempt the practice questions on Chapter 6: Quadratic Equations, Exercise 2: EXERCISE 6.2 with hints and solutions to strengthen your understanding. Understanding ISC Mathematics Class 11 Volume 1 solutions are prepared by Experienced Embibe Experts.

Questions from M L Aggarwal Solutions for Chapter: Quadratic Equations, Exercise 2: EXERCISE 6.2 with Hints & Solutions

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.2>Q 19

Solve the equation $\frac{\sqrt{a + x} - \sqrt{a - x}}{\sqrt{a + x} + \sqrt{a - x}} = \frac{x}{a}, a \neq 0$ .

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.2>Q 20

Solve the equation ${(x + \frac{1}{x})}^{2} - 2 (x - \frac{1}{x} + 4) = 11$ .

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.2>Q 20

Solve the equation $12 x^{4} - 56 x^{3} + 89 x^{2} - 56 x + 12 = 0$ .

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.2>Q 21

Solve the equation ${(x^{2} + 2)}^{2} + 8 x^{2} = 6 x (x^{2} + 2)$ .

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.2>Q 22

Solve the simultaneous equations $\sqrt{\frac{x}{y}} + \sqrt{\frac{y}{x}} = 2 \frac{1}{2}, x + y = 10$

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.2>Q 22

Solve the simultaneous equations $x^{2} + y^{2} = 10, x + y = 4$ .

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.2>Q 23

An express train makes a run of $240 km$ at a certain speed. Another train whose speed is $12 km / h$ less takes an hour longer to make the same trip. Find the speed of the express train in $km / h$ .

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.2>Q 24

A trader bought a number of articles for $₹ 1200$ . Ten were damaged and he sold each of the rest at $₹ 2$ more than what he paid for, thus clearing a profit of $₹ 60$ on the whole transaction. Find the number of articles he bought.

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