CTET 2 Math and Science Jul 2013 Paper

Question : 56 of 120

Marks: +1, -0

p =3^{2000} + 3^{-2000}

and

q =3^{2000} - 3^{-2000}

, then the value of

p^{2} -q^{2}

Solution:

{p}=3^{2000}+3^{-2000},{q}=3^{2000}-3^{-2000}

Let

x=2000

⇒p=3^{x}+3^{-x},q=3^{x}-3^{-x}

Now,

p^{2}-q^{2}

=(p+q)(p-q)

=(3^{x}+3^{X}+3^{x}-3^{X})[3^{x}+3^{-x}-(3^{x}-3^{-x})]

=(3^{x}+3^{x})[z^{x}+3^{-x}-z^{x}+3^{-x}]

=(3^{x}+3^{x})(3^{-x}+3^{-x})

=(2×3^{x})(2×3^{-x})

=4×3^{x}×\;\;{1}/{3^{x}}=4

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