Question

if x=1/3-2√2 and y=1/3+2√2 then valuex^2y^2​

Answer 1

Answer:

$\sf{The \ value \ of \ x^{2}y^{2} \ is \ 1.}$

Given:

$\sf{x=\dfrac{1}{3-2\sqrt2} \ and \ y=\dfrac{1}{3+2\sqrt2}}$

To find:

$\sf{The \ value \ of \ x^{2}y^{2}.}$

Solution:

$\sf{\leadsto{x^{2}y^{2}}}$

$\sf{\leadsto{(xy)^{2}}}$

$\sf{\leadsto{[(\dfrac{1}{3-2\sqrt2})\times(\dfrac{1}{3+2\sqrt2})]^{2}}}$

$\sf{\leadsto{(\dfrac{1}{9-8})^{2}}}$

$\sf{\leadsto{(\dfrac{1}{1})^{2}}}$

$\sf{\leadsto{1}}$

$\sf\purple{\tt{\therefore{The \ value \ of \ x^{2}y^{2} \ is \ 1.}}}$

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Extra information:

• $\sf{a^{m}\times \ a^{n}=a^{m+n}}$

• $\sf{\dfrac{a^{m}}{a^{n}}=a^{m-n}}$

• $\sf{(ab)^{m}=a^{m}b^{m}}$