Subject
Quantitative Aptitude
Topic
Number
The sum of two numbers is 15 and the sum of their squares is 113 Find the numbers.
The sum of two numbers is 15 and the sum of their squares is 113 Find the numbers.
ক)
6 and 9খ)
7 and 8গ)
10 and 5ঘ)
None of theseExplanation
The sum of the numbers is 15 x + y = 15 or y = (15 - x); we can use this for substitution: "The sum of the squares is 113" x2 + y2 = 113 Substitute (15-x) for y in the above equation x2 + (15-x)2 = 113 x2 + 225 - 30x + x2 = 113 Arrange as a quadratic equation: x2+ x2 - 30x + 225 - 113 = 0 2x2 - 30x + 112 = 0 Simplify, divide by 2 x2 - 15x+56=0 => x2 -8x - 7x + 56 =0 => x(x-8)-7(x-8)=0 => (x-8)(x-7)=0 so, x= 8 or 7 when x = 8, then y=15-8=7 or, when x = 7, then y=15-7=8Related questions
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