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One number is 2 larger than another number. the sum of their squares is 100. find the numbers
4 months ago
Q:
one number is 2 larger than another number. the sum of their squares is 100. find the numbers
Accepted Solution
A:
x= first number
x+2= second number
x^2 + (x + 2)^2= 100
square the parentheses
x^2 + [(x + 2)(x + 2)]= 100
x^2 + x^2 + 2x + 2x + 4= 100
combine like terms
2x^2 + 4x + 4= 100
subtract 100 from both sides
2x^2 + 4x - 96= 0
factor
2(xβ6)(x+8)=0
set each parentheses equal to 0
x-6= 0
x= 6
OR
x+8= 0
x= -8
CHECK:
x^2 + (x + 2)^2= 100
(6)^2 + (6 + 2)^2= 100
36 + (8)^2= 100
36 + 64= 100
100= 100
x^2 + (x + 2)^2= 100
(-8)^2 + (-8 + 2)^2= 100
64 + (-6)^2= 100
64 + 36= 100
100= 100
ANSWER: x= 6 or x= -8
Hope this helps! :)