Question

to find (x+1)^32, pls solve need help​

Answer 1

Step-by-step explanation:

We have,

$x = \frac{2}{( \sqrt{3} + 1)( \sqrt[4]{3} + 1)( \sqrt[8]{3} + 1)( \sqrt[16]{3} + 1) }$

$\implies \: x = \frac{2( \sqrt[16]{3} - 1) }{( \sqrt{3} + 1)( \sqrt[4]{3} + 1)( \sqrt[8]{3} + 1)( \sqrt[16]{3} + 1) ( \sqrt[16]{3} - 1) }$

$\implies \: x = \frac{2( \sqrt[16]{3} - 1) }{( \sqrt{3} + 1)( \sqrt[4]{3} + 1)( \sqrt[8]{3} + 1)( \sqrt[8]{3} - 1) }$

$\implies \: x = \frac{2( \sqrt[16]{3} - 1) }{( \sqrt{3} + 1)( \sqrt[4]{3} + 1)( \sqrt[4]{3} - 1) }$

$\implies \: x = \frac{2( \sqrt[16]{3} - 1) }{( \sqrt{3} + 1)( \sqrt{3} - 1) }$

$\implies \: x = \frac{2( \sqrt[16]{3} - 1) }{(3 - 1) }$

$\implies \: x = \frac{2( \sqrt[16]{3} - 1) }{2 }$

$\implies \: x = \sqrt[16]{3} - 1$

Now,

$(x + 1)^{32} = ( \sqrt[16]{3} - 1 + 1)^{32} = {( \sqrt[16]{3} )}^{32} = {3}^{2} = 9$