Question

If a+b = 7 and ab= 12 then a⁴-b⁴
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Answer 1

Answer:

The answer is 175

Step-by-step explanation:

Given $a+b=7$ and $ab=12$

Thus

$a^4-b^4=(a^2-b^2)(a^2+b^2)\\=(a-b)(a+b)[(a+b)^2-2ab]\\=(a-b)(7)(49-24)=175(a-b)$

Now

$a-b=\sqrt{(a-b)^2}=\sqrt{a^2+b^2-2ab}\\=\sqrt{(a+b)^2-4ab}=\sqrt{49-48}=\sqrt 1=1$

Hence $a^4-b^4=175$

(Assumption is $a>b$)