The sum of two numbers is 9 and sum of their squares is 41 . Taking one number as x , form an equation in x and solve it to find the numbers.

Let the two numbers be x & 9 - x , so their sum would be 9 . Given that x 2 + ( 9 - x ) 2 = 41 x 2 + 81 + x 2 - 18 x = 41 2 x 2 - 18 x + 40 = 0 x 2 - 9 x + 20 = 0 Comparing the above equation with a x 2 + b x + c = 0 we have, a = 1 , b = - 9 , c = 20 So the values of x are given by - - 9 ± - 9 2 - 4 × 20 × 1 2 × 1 x = 9 ± 81 - 4 × 20 2 x = 9 ± 1 2 x = 5 or 4 Hence, the required numbers are 5 & 4 .

E M B I B E

Understanding ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Exercise 5.5>Q 2

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IMPORTANT

Earn 100

Find two consecutive even natural numbers such that the sum of their squares is $340$ .

Important Questions on Quadratic Equations in One Variable

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IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Exercise 5.5>Q 2

Find two consecutive odd positive integers, sum of whose squares is

394

.

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IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Exercise 5.5>Q 3

The sum of two numbers is

9

and sum of their squares is

41

. Taking one number as

= 2 x = 2 (6) = 12

, form an equation in

x

and solve it to find the numbers.

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IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Exercise 5.5>Q 4

Five times a certain whole number is equal to three less than twice the square of the number. Find the number.

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IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Exercise 5.5>Q 5

The sum of two natural numbers is $8$ and the difference of their reciprocals is $\frac{2}{15}$ . Find the numbers.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Exercise 5.5>Q 6

The difference of the squares of two positive numbers is $45$ . The square of the smaller number is four times the larger number. Find the numbers.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Exercise 5.5>Q 7

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.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Exercise 5.5>Q 8

Find three successive even natural numbers, the sum of whose squares is