If #a + b = 8# and #a^2 + b^2 = 60#, what is #a^2b^2# ?

2 Answers
Narad T.
Feb 8, 2018

The answer is #=4#

Explanation:

#(a+b)=8#

and

#a^2+b^2=60#

Therefore,

#(a+b)^2=8^2=64#

But,

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

So,

#64=60+2ab#

#2ab=64-60=4#

#ab=4/2=2#

and

#a^2b^2=(ab)^2=2^2=4#

Jim G.
Feb 8, 2018

#a^2b^2=4#

Explanation:

#"given "a+b=8#

#"then "(a+b)^2=8^2=64#

#"now "(a+b)^2=a^2+2ab+b^2#

#rArra^2+2ab+b^2=64#

#"substitute "a^2+b^2=60#

#rArr60+2ab=64#

#rArr2ab=64-60=4#

#rArrab=4/2=2#

#color(blue)"square both sides"#

#rArr(ab)^2=2^2#

#rArra^2b^2=4#

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