Question

The sum of the squares of two consecutive numbers is equal to 145. Find the two numbers

Answer 1

x and x+1 be the nos.
x^2+(x+1)^2=145
x^2+x^2+1+2x=145
2x^2+2x+1=145
2x^2+2x=144
x^2+x=72
evaluate this equation
answer will be -9 and 8

Answer 2

x and x+1 are the numbers

x^2+(x+1)^2=145

x^2+x^2+2x+1=145

2x^2+2x+1-145=0

2x^2+2x-144=0

divide all terms by 2

x^2+x-72=0

factor (9*8=72)

factor (9*8=72)

(x+9)(x-8)=0

x+9=0

x=-9 and x+1=-8, -8 and -9

x-8=0

x=8 and x+1=9, 8 and 9

you have 2 solutions


Thanq

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