Question

if x is equal to 3 + root 8 and Y is equal to 3 minus root then one upon X square + 1 upon y square is equal to​

Answer 1

Correct question: If x = 3 + √8 and y = 3 - √8. Find the value of 1/x² + 1/y².

Answer:

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

Step-by-step explanation:

Given that -

x = 3 + √8

Squaring both the sides-

⇒ x² = (3 + √8)²

⇒ x² = (3)² + 2 * 3 * √8 + (√8)²

⇒ x² = 9 + 6√8 + 8

⇒ x² = 17 + 6√8

And,

y = 3 - √8

Squaring both the sides-

⇒ y² = (3 - √8)²

⇒ y² = (3)² - 2 * 3 * √8 + (√8)²

⇒ y² = 9 - 6√8 + 8

⇒ y² = 17 - 6√8

Now, we have to find:

$\implies \sf \frac{1}{x {}^{2} } + \frac{1}{y {}^{2} } \\ \\ \implies \sf \frac{1}{17 + 6 \sqrt{8} } + \frac{1}{17 - 6 \sqrt{8} } \\ \\ \implies \sf \frac{17 - 6 \sqrt{8} + 17 + 6 \sqrt{8} }{(17 + 6 \sqrt{8})(17 - 6 \sqrt{8} )} \\ \\ \implies \sf \frac{17 + 17}{(17) {}^{2} - (6 \sqrt{8} ) {}^{2} } \\ \\ \implies \sf \frac{34}{289 - 288} \\ \\ \implies \sf 34$

Hence,

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

Answer 2

Correction:

If x is equal to 3+√8 and this equal to 3-√8,then find 1/x²+1/y²?

Answer:

Given

x = 3+√8

and, y = 3-√8

First,let us find 1/x and 1/y

On rationalising,

$\mathbf{ \frac{1}{x} = \frac{1}{3 + \sqrt{8}} = \frac{1}{3 + \sqrt{8}} \times \frac{3 - \sqrt{8} }{3 - \sqrt{8} } = \frac{3 - \sqrt{8} }{3 {}^{2} - \sqrt{8 {}^{2} } } = \frac{3 - \sqrt{8} }{9 - 8} = 3 - \sqrt{8} }$

$\mathbf{ \frac{1}{y} = \frac{1}{3 - \sqrt{8} } = \frac{1}{3 - \sqrt{8}} \times \frac{3 + \sqrt{8} }{3 + \sqrt{8} } = \frac{3 + \sqrt{8} }{3 {}^{2} - \sqrt{8 {}^{2} } } = 3 + \sqrt{8} }$

Now,

$\mathbf{ \frac{1}{x {}^{2} } + \frac{1}{y {}^{2} } } \\ \\ \mathbf{ = (\frac{1}{x} ) {}^{2} + ( \frac{1}{y}) {}^{2} } \\ \\ = \mathbf{(3 + \sqrt{8} ) {}^{2} + (3 - \sqrt{8} ) {}^{2}} \\ \\ \mathbf{ = 9 +8 + 6 \sqrt{8} + 9 + 8 - 6 \sqrt{8} } \\ \\ = \mathbf{17 + 17} \\ \\ = \mathbf{34}$

Thus,

$\mathbf{ \huge \boxed{ \boxed{ \frac{1}{x {}^{2} \: } + \frac{1}{y {}^{2} } = 34 }}}$