Question

plz answer these 2 question with full explanation​

Answer 1

Answer:

Q1. The ans is 34 the solution photo is above

2.ans is 8

Answer 2

Question: If x = 3 - 2√2, find x² + 1/x².

Answer:

$\large{\underline{\boxed{\sf x {}^{2} + \frac{1}{x {}^{2} } = 34}}}$

Step-by-step explanation:

$\sf x = 3 - 2 \sqrt{2} \\ \\ \implies \sf \frac{1}{x} = \frac{1}{3 - 2 \sqrt{2} } \\ \\ \implies \sf \frac{1}{3 - 2 \sqrt{2} } \times \frac{3 + 2 \sqrt{2} }{3 + 2 \sqrt{2} } \\ \\ \implies \sf \frac{3 + 2 \sqrt{2} }{(3) {}^{2} - (2 \sqrt{2} ) {}^{2} } \\ \\ \implies \sf \frac{3 + 2 \sqrt{2} }{9 - 8} \\ \\ \implies \sf \frac{1}{x} = 3 + 2 \sqrt{2}$

Now, find x + 1/x -

$\small \implies \sf x + \frac{1}{x} = 3 - 2 \sqrt{2} + 3 + 2 \sqrt{2} \\ \\ \implies \sf x + \frac{1}{x} = 3 + 3 \\ \\ \implies \sf x + \frac{1}{x} = 6 \\ \\ \bf on \: squaring \: both \: sides - \\ \\ \implies \sf (x + \frac{1}{x} ) {}^{2} = (6) {}^{2} \\ \\ \implies \sf x {}^{2} + \frac{1}{x {}^{2} } + 2 = 36 \\ \\ \implies \sf x {}^{2} + \frac{1}{x {}^{2} } = 36 - 2 \\ \\ \boxed{ \bf x {}^{2} + \frac{1}{x {}^{2} } = 34}$

Hence, the answer is 34.

______________________________

Question: If x = 1 - √2 , find (x - 1/x)³.

Answer:

$\large{\underline{\boxed{\sf (x - \frac{1}{x}) {}^{3} =8}}}$

Step-by-step explanation:

$\sf x = 1 - \sqrt{2} \\ \\ \implies \sf \frac{1}{x} = \frac{1}{1 - \sqrt{2} } \\ \\ \implies \sf \frac{1}{x} = \frac{1}{ 1 - \sqrt{2}} \times \frac{1 + \sqrt{2} }{1 + \sqrt{2} } \\ \\ \implies \sf \frac{1}{x} = \frac{1 + \sqrt{2} }{(1) {}^{2} - ( \sqrt{2}) {}^{2} } \\ \\ \implies \sf \frac{1}{x} = \frac{1 + \sqrt{2} }{1 - 2} \\ \\ \implies \sf \frac{1}{x} = \frac{1 + \sqrt{2} }{ - 1} \\ \\ \implies \sf \frac{1}{x} = - (1 + \sqrt{2} )$

Now, find (x - 1/x) -

$\implies \sf x - \frac{1}{x} = 1 - \sqrt{2} + 1 + \sqrt{2} \\ \\ \implies \sf x - \frac{1}{x} = 1 + 1 \\ \\ \implies \sf x - \frac{1}{x} = 2 \\ \\ \bf on \: cubing \: both \: sides - \\ \\ \implies \sf (x - \frac{1}{x}) {}^{3} = (2) {}^{3} \\ \\ \underline{ \boxed{\bf (x - \frac{1}{x}) {}^{3} =8}}$