Question

If a2+b2=13 and ab=6 finda2-b2

Answer 1

Answer:

a^2 - b^2 = 5

Step-by-step explanation:

Given :

$a^2 + b^2=13\\\\\\ab=6\\\\\\a^2-b^2 = ~find~$

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$(a+b)^2=a^2+b^2+2ab\\\\\\(a+b)^2=13+2(6)\\\\\\(a+b)^2=13+12\\\\\\(a+b)^2=25\\\\\\a+b=\sqrt{25}\\\\\\a+b=5$

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$(a-b)^2=a^2+b^2-2ab\\\\\\(a-b)^2=13-2(6)\\\\\\(a-b)^2=13-12\\\\\\(a-b)^2=1\\\\\\a-b=\sqrt{1}\\\\\\a-b=1$

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$a^2-b^2=(a+b)(a-b)\\\\\\a^2-b^2=(5)(1)\\\\\\a^2-b^2=5$