Question

a^2+b^2=169 and ab=60 find a^2-b^2​

Answer 1

Answer:

2ab=(a^2+b^2)-(a-b)^2

2(60)=169-(a-b)^2

(a-b)^2=49

a-b=7 then b=a-7

since ab=60 then b=60/a

equating both b

a-7=60/a

a^2-7a-60=0

equating a=12 , -5

let a=12 then b=a-7=12-7=5

finally a^2-b^2=(12^2) - (5^2)=144-25

=119