Question 1018213
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Find the value of  8ab (a2+b2) when  a+b=root 5 and a-b = root 3
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a + b = {{{sqrt(5)}}},   (1)
a - b = {{{sqrt(3)}}}.   (2)

By adding equations (1) and (2), you get a = {{{(sqrt(5)+sqrt(3))/2}}}.

By subtracting (2) from (1), you get b = {{{(sqrt(5)-sqrt(3))/2}}}.

It implies that {{{a^2 + b^2}}} = {{{1/4}}}.{{{((sqrt(5)+sqrt(3))^2 + (sqrt(5)-sqrt(3))^2)}}} = {{{1/4}}}.{{{(5+3+5-3)}}} = {{{10/4}}} = 2.5.

Next, a*b = {{{1/4}}}.{{{(sqrt(5)+sqrt(3))*(sqrt(5)-sqrt(3))}}} = {{{1/4}}}.{{{(5-3)}}} = {{{1/2}}}.

Therefore, {{{8ab*(a^2+b^2)}}} = {{{8*(1/2)*2.5}}} = 10.

<U>Answer</U>.  {{{8ab*(a^2+b^2)}}} = 10.
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