If #(a+b)^2=9# and #(a-b)^2=49#, what is the value of #a^2+b^2#?

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Answer 1 · 2018-05-17T02:52:19

See a solution process below:

First, we can expand the first equation as:

#(a + b)^2 = 9#

#a^2 + 2ab + b^2 = 9#

Next, we can expand the second equation as:

#(a - b)^2 = 49#

#a^2 - 2ab + b^2 = 49#

Then, we can add the left side of each equation and the right side of each equation giving:

#a^2 + 2ab + b^2 + a^2 - 2ab + b^2 = 9 + 49#

#a^2 + a^2 + 2ab - 2ab + b^2 + b^2 = 58#

#2a^2 + 0 + 2b^2 = 58#

#2a^2 + 2b^2 = 58#

#2(a^2 + b^2) = 58#

#(2(a^2 + b^2))/color(red)(2) = 58/color(red)(2)#

#(color(red)(cancel(color(black)(2)))(a^2 + b^2))/cancel(color(red)(2)) = 29#

#a^2 + b^2 = 29#