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Concept of Inequality

If x=7+43 and...

Question

If $x = 7 + 4 \sqrt{3}$ and xy =1, then $\frac{1}{x^{2}} + \frac{1}{y^{2}} =$

(a) 64

(b) 134

(c) 194

(d) 1/49

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Solution

Given that,

Hence is given as

We need to find

We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Since so we have

Therefore,

Hence the value of the given expression is.

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Similar questions

If $x = 7 + 4 \sqrt{3}$ and xy = 1, then $\frac{1}{x^{2}} + \frac{1}{y^{2}} =$

x = (7 + 4 \sqrt{3}), then (x + \frac{1}{x})

8 \sqrt{3}

(b) 14
(c) 49
(d) 48

If $x + \frac{1}{x} = 4, t h e n x^{4} + \frac{1}{x^{4}} =$

$I f 3 x - 7 y = 10 a n d x y = - 1, f i n d t h e v a l u e o f 9 x^{2} + 49 y^{2}$

x + \frac{1}{x} = 2

x^{3} + \frac{1}{x^{3}} =

(a) 64

(b) 14

(c) 8

(d) 2

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