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Polynomials

If the value ...

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If the value of $(6 + \sqrt{5}) \times (6 - \sqrt{5}) = 6 x - 5 y$ then the value of $x =$ and $y =$ .

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\frac{x + 3}{4} + \frac{x - 2}{6} = \frac{6 x + 5}{14}

, then the value

x = 5 + 2 \sqrt{6}

y = 5 - 2 \sqrt{6}

then find the value of

\frac{1}{x^{2}} + \frac{1}{y^{2}}

.

\frac{x}{y} = \frac{13}{6}

\frac{3 x + 5 y}{3 x - 5 y}

= \frac{k}{3}

.
Find the value of

k

{log}_{5} x = y

, then value of

5^{5 y}

(6)^{15} \times (10)^{5} \times (15)^{6} = 2^{x} \times 3^{y} \times 5^{z}

then find the value of x + y + z.

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