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a+b=5

a

a

^{2}-b^{2}=45a

^{2}-b^{2}=(a+b)(a-b)=5(a-b)=45a+b=5

a -b=9

add them

2a=14 so a=7

subtract them

2b=-4

b=-2

this question comes from the words problems

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Wilton, CT

a+b=5

a^{2}-b^{2}=45

a

a^{2}-b^{2}=(a+b)(a-b)=5(a-b)=45

a+b=5

a -b=9

add them

2a=14 so a=7

subtract them

2b=-4

b=-2

Seattle, WA

a+b=5

a^{2}-b^{2}=45

System of non-linear equations: (two unknowns in two equations) Solve by iterative substitution.

b = 5-a

a^{2}-(5-a)^{2}=45

a^{2}-(25-10a+a^{2}) = 45

10a-25=45

10a=70

a=7

b=5-a

b=5-7

b=-2

Saugus, MA

just a thought looking at the problem; what perfect square is close to 45 ? 49 !!!

49-45=4, another perfect square(2x2)

looking at 7 and 2, their sum is not 5, but 7 and -2 have a sum of 5

(7^2)-(-2)^2=49-4=45 and 7+(-2)=5

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