Solve x - 2 x + 2 + x + 2 x - 2 = 4 .

The given equation is x - 2 x + 2 + x + 2 x - 2 = 4 Taking LCM and using ( a - b ) 2 + ( a + b ) 2 = 2 ( a 2 + b 2 ) we get, ( x - 2 ) 2 + ( x + 2 ) 2 x 2 - 4 = 4 2 ( x 2 + 4 ) = 4 x 2 - 16 2 x 2 - 24 = 0 is a quadratic equation whose roots are, x 2 = 12 ⇒ x = ± 2 3 are the required solutions.

Solve x - 1 x - 2 + x - 3 x - 4 = 3 1 3 .

The given equation is x - 1 x - 2 + x - 3 x - 4 = 3 1 3 Taking LCM we get, ( x - 1 ) ( x - 4 ) + ( x - 2 ) ( x - 3 ) ( x - 2 ) ( x - 4 ) = 10 3 2 x 2 - 10 x + 10 x 2 - 6 x + 8 = 10 3 Cross multiplying we get, 6 x 2 - 30 x + 30 = 10 x 2 - 60 x + 80 4 x 2 - 30 x + 50 = 0 is a quadratic equation whose roots are, x = - - 30 ± - 30 2 - 4 × 4 × 50 2 × 4 x = 30 ± 100 8 x = 30 ± 10 8 Therefore, x = 5 , 2 . 5 are the required solutions.

E M B I B E

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.1>Q 11

MEDIUM

11th ICSE

IMPORTANT

Earn 100

The sum of the squares of two consecutive positive even integers is $340$ . Find the integers.

Important Questions on Quadratic Equations

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IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.1>Q 12

A two digit number is four times the sum and three times the product of its digits. Find the number.

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.1>Q 13

The hypotenuse of a right angled triangle is

17 cm

and the difference between the other two sides is

7 cm

long. Find the lengths of the two unknown sides.

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.1>Q 14

Originally a rectangle is twice as long as it is wide. When

4 m

were added to its length and

3 m

subtracted from its width, the resulting rectangle had an area of

600 m^{2}

. Find the dimensions of the new rectangle.

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IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.1>Q 15

A rectangular garden of dimensions

10 m \times 16 m

is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is

120 Sq . m

, find its width.

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IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.1>Q 16

Two years ago, a man's age was three times the square of his son's age. In three years time, his age will be four times his son's age. Find their present ages.

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IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.1>Q 17

A piece of cloth costs