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If $x = 4 − 15,$ then what is the value of $x 2 − 1 x 2$ ?

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− 1613

− 1115

1615

− 1615

answer is B.

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Detailed Solution

The given equation is,

x = 4 − 15,

Substitute the value of

x

x 2 − 1 x 2 .

Therefore, we can simplify it as,

x 2 − 1 x 2 = 4 − 15 2 − 1 4 − 15 2

⇒ x 2 − 1 x 2 = 16 + 15 − 815 − 1 16 + 15 − 815 a − b 2 = a 2 + b 2 − 2 a b

⇒ x 2 − 1 x 2 = 31 − 815 − 1 31 − 815

Use the rationalization method to rationalize the denominator of RHS.
Therefore, we can simplify it as,
Question Image

Thus, if

x = 4 − 15,

then the value of

x 2 − 1 x 2 = − 1615 .

Hence, option 2 is the correct option.

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