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# 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.

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

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1. Given:

Sum of two number = 9

Let us consider first number be ‘x’

Second number be ‘9 – x’

So according to the question,

(x)2 + (9 – x)2 = 41

x2 + 81 – 18x + x2 – 41 = 0

2x2 – 18x + 40 = 0

Divide by 2, we get

x2 – 9x + 20 = 0

Let us factorize,

x2 – 4x – 5x + 20 = 0

x(x – 4) – 5(x – 4) = 0

(x – 4) (x – 5) = 0

So,

(x – 4) = 0 or (x – 5) = 0

x = 4 or x = 5

When x = 4, then

First number = x = 4

Second number = 9 – x = 9 – 4 = 5

When x = 5, then

First number = x = 5

Second number = 9 – x = 9 – 5 = 4

∴ The required numbers are 4 and 5.

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