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 ‘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.