The sum of two intergers is 5.The difference between their squares is 45 determine the numbers

Question

this question comes from the words problems

Answer 1

a+b=5
a²-b²=45

a²-b²=(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

 

 

Answer 2

a+b=5

a²-b²=45

 

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

 

b = 5-a

a²-(5-a)²=45

a²-(25-10a+a²) = 45

10a-25=45

10a=70

a=7

 

b=5-a

b=5-7

b=-2

 

 

 

Answer 3

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