Question

a= 7+ √12 & b= 7-2√12, then (a^3+b^3) is
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Answer 1

Answer:

$\large{\underline{\boxed{\sf a {}^{3} + {b}^{3} = 302 \sqrt{7}}}}$

Step-by-step explanation:

Given that -

a = √7 + 2√12

b = √7 - 2√12

Now, find the value of (a + b)-

⇒ a + b = √7 + 2√12 + √7 - 2√12

⇒ a + b = √7 + √7

⇒ a + b = 2√7

Also, find the value of (ab)-

⇒ ab = (√7 + 2√12)(√7 - 2√12)

⇒ ab = (√7)² - (2√12)²

⇒ ab = 7 - 48

⇒ ab = -41

Consider (a + b)-

$\begin{gathered} \implies \sf a + b = 2 \sqrt{7} \\ \\ \bf on \: cubing \: both \: sides : \\ \\ \implies \sf (a + b) {}^{3} = {(2 \sqrt{7})}^{3} \\ \\ \implies \sf a {}^{3} + {b}^{3} + 3ab(a + b) = 56 \sqrt{7} \\ \\ \implies \sf a {}^{3} + {b}^{3} +3( - 41)(2 \sqrt{7} ) = 56 \sqrt{7} \\ \\ \implies \sf a {}^{3} + {b}^{3} - 246 \sqrt{7} = 56 \sqrt{7} \\ \\ \implies \sf a {}^{3} + {b}^{3} = 56 \sqrt{7} + 246 \sqrt{7} \\ \\ \boxed{ \bf \therefore \: a {}^{3} + {b}^{3} = 302 \sqrt{7}}\end{gathered}$

Thankyou :)

Answer 2

Answer:

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