Solve for x , 2 x - 3 x - 1 - 4 ( x - 1 ) 2 x - 3 = 3 ; x ≠ 1 , 3 2

We have, 2 x - 3 x - 1 - 4 ( x - 1 ) 2 x - 3 = 3 ⇒ 2 x - 3 2 - 4 x - 1 2 x - 1 2 x - 3 = 3 ⇒ 4 x 2 - 12 x + 9 - 4 x 2 - 2 x + 1 2 x 2 - 3 x - 2 x + 3 = 3 ⇒ 4 x 2 - 12 x + 9 - 4 x 2 + 8 x - 4 2 x 2 - 5 x + 3 = 3 ⇒ 5 - 4 x 2 x 2 - 5 x + 3 = 3 ⇒ 6 x 2 - 15 x + 9 = 5 - 4 x ⇒ 6 x 2 - 11 x + 4 = 0 ⇒ 6 x 2 - 8 x - 3 x + 4 = 0 ⇒ 2 x 3 x - 4 - 1 3 x - 4 = 0 ⇒ 3 x - 4 2 x - 1 = 0 ⇒ 3 x - 4 = 0 o r 2 x - 1 = 0 ⇒ x = 4 3 o r x = 1 2 Therefore, value of x are 4 3 , 1 2 .

Solve for x : 1 x + 1 + 2 x + 2 = 4 x + 4 ; x ≠ - 1 , - 2 , - 4

We have, 1 x + 1 + 2 x + 2 = 4 x + 4 ⇒ x + 2 + 2 x + 1 ( x + 1 ) ( x + 2 ) = 4 x + 4 ⇒ x + 2 + 2 x + 2 ( x + 1 ) ( x + 2 ) = 4 x + 4 ⇒ 3 x + 4 x 2 + 3 x + 2 = 4 x + 4 ⇒ 4 x 2 + 12 x + 8 = 3 x + 4 x + 4 ⇒ 4 x 2 + 12 x + 8 = 3 x 2 + 12 x + 4 x + 16 ⇒ x 2 - 4 x - 8 = 0 Comparing this equation with a x 2 + b x + c = 0 , we have, a = 1 , b = - 4 , c = - 8 . Now, we have. x = - b ± b 2 - 4 a c 2 a ⇒ x = - - 4 ± - 4 2 - 4 × 1 × - 8 2 × 1 ⇒ x = 4 ± 16 + 32 2 ⇒ x = 4 ± 48 2 ⇒ x = 4 ± 4 3 2 ⇒ x = 2 ± 2 3 .

E M B I B E

New Mathematics for Class X>Chapter 4 - Quadratic Equations>REVISION EXERCISE

H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Quadratic Equations, Exercise 6: REVISION EXERCISE

Author:H K Dass, Rama Verma & Bhagwat Swarup Sharma

H K Dass Mathematics Solutions for Exercise - H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Quadratic Equations, Exercise 6: REVISION EXERCISE

Attempt the free practice questions on Chapter 4: Quadratic Equations, Exercise 6: REVISION EXERCISE with hints and solutions to strengthen your understanding. New Mathematics for Class X solutions are prepared by Experienced Embibe Experts.

Questions from H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Quadratic Equations, Exercise 6: REVISION EXERCISE with Hints & Solutions

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 4 - Quadratic Equations>REVISION EXERCISE>Q 11

Solve for $x$ ,

$\frac{2 x - 3}{x - 1} - \frac{4 (x - 1)}{2 x - 3} = 3; x \neq 1, \frac{3}{2}$

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 4 - Quadratic Equations>REVISION EXERCISE>Q 20

Find the values of $k$ for which roots of the equation $x^{2} - 8 k x + 2 k = 0$ are equal $(k \neq 0)$ .

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 4 - Quadratic Equations>REVISION EXERCISE>Q 14

Solve for $x :$

$\frac{1}{x + 1} + \frac{2}{x + 2} = \frac{4}{x + 4}; x \neq - 1, - 2, - 4$

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 4 - Quadratic Equations>REVISION EXERCISE>Q 10

Two taps together can fill a tank in $9 \frac{3}{8}$ $hrs$ . The tap of larger diameter takes $10$ $hrs$ less than the smaller tap to fill the tank separately. Find the time in which each tap can fill the tank separately.

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 4 - Quadratic Equations>REVISION EXERCISE>Q 15

Solve the following equation for $x$

$9 x^{2} - 9 (a + b) x + (2 a^{2} + 5 a b + 2 b^{2}) = 0$

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 4 - Quadratic Equations>REVISION EXERCISE>Q 16

The sum of the squares of two consecutive odd natural numbers is $130 .$ Find the numbers.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 4 - Quadratic Equations>REVISION EXERCISE>Q 17

The product of Tanay's age (in years) five years ago and his age ten years later is $16 .$ Determine Tanay's present age in the number of years.

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 4 - Quadratic Equations>REVISION EXERCISE>Q 18

Three consecutive positive integers are taken such that the sum of the square of the first and the product of the other two is $154 .$ Find the integers.

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