Question

the sum of two number is 9 and the sum of their square is 41 .Taking one numberas x , form an equation in x and solve it to find the number.

Answer 1

let be two numbers are x and y
according to the question
x+y=9
x=9-y....(1)
x²+y²=41
putting the value of x in the equation
(9-y) ²+y²=41
81-18y+y²+y²=41
2y²-18y+81-41=0
2y²-18y+40=0
dividing by 2
y²-9y+20=0
spitting middle term
y²-5y-4y+20=0
y(y-5) -4(y-5)=0
(y-4)(y-5)=0
y-4=0 and y-5=0
so, y=4 or 5
putting the value of y in equation (1)
so value of x=5 or 4
so two numbers 4 and 5 or 5 and 4
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