Book:- ML aggarwal, Avichal publication, class10th, quadratic equation in one variable, chapter 5, exercise 5.5

This is an important ques and asked in

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

Question no.3 , ML Aggarwal, chapter 5, exercise 5.5, quadratic equation in one variable, ICSE board,

Given:

Sum of two number = 9

Let us consider first number be â€˜xâ€™

Second number be â€˜9 â€“ xâ€™

So according to the question,

(x)

^{2}Â + (9 â€“ x)^{2}Â = 41x

^{2}Â + 81 â€“ 18x + x^{2}Â â€“ 41 = 02x

^{2}Â â€“ 18x + 40 = 0Divide by 2, we get

x

^{2}Â â€“ 9x + 20 = 0Let us factorize,

x

^{2}Â â€“ 4x â€“ 5x + 20 = 0x(x â€“ 4) â€“ 5(x â€“ 4) = 0

(x â€“ 4) (x â€“ 5) = 0

So,

(x â€“ 4) = 0 or (x â€“ 5) = 0

x = 4 or x = 5

When x = 4, then

First number = x = 4

Second number = 9 â€“ x = 9 â€“ 4 = 5

When x = 5, then

First number = x = 5

Second number = 9 â€“ x = 9 â€“ 5 = 4

âˆ´ The required numbers are 4 and 5.