Question

a=√7+2√12,b=√7-2√12 than(a^3+b^3)​

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)-

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

Answer 2

Hope it helps u..........