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Find two numbers such that the sum of the numbers is 12 and the sum of their squares is 74.

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in Mathematics - Class 10 by (506k points)
Find two numbers such that the sum of the numbers is 12 and the sum of their squares is 74.

(a) 84

(b) 75

(c) 66

(d) 48

The question was asked in final exam.

My question comes from Solution of Quadratic Equation by Factorisation in chapter Quadratic Equation of Mathematics – Class 10

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Right option is (b) 75

Explanation: Sum of the numbers is 12.

Let one number be x. Other number is 12-x.

Sum of their squares = 74

x^2+(12-x)^2=74

x^2+144+x^2-24x=74

2x^2-24x+144-74=0

2x^2-24x+70=0

x^2-12x+35=0

x^2-7x-5x+35=0

x(x-7)-5(x-7)=0

(x-7)(x-5)=0

x=7, 5

The number is 57 or 75.

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