Question

(y-1/y)^3＝27,then find the value of y^3-1/y^3​. pls find the answer and tell me fast .

Answer 1

Answer:

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Answer 2

Answer:

$y^{3}-(\frac{1}{y})^{3}=33$

Step-by-step explanation:

As per the question,

Given:

$(y-\frac{1}{y})^{3}=(27)$

Now on solving this equation, we get

$(y-\frac{1}{y})=(27)^{\frac{1}{3}}$

$(y-\frac{1}{y})=(27)^{\frac{1}{3}}$

$(y-\frac{1}{y}) =(3^{3})^\frac{1}{3}$

$(y-\frac{1}{y}) = 3$

As we have to find the value of $y^{3}-\frac{1}{y^{3}}$

Now we know the identity

$(a-b)^{3}= a^{3} -3a^{2}b+3ab^{2}-b^{3}$

Therefore, replace a=y and b=1/y

$(y-\frac{1}{y})^{3}= y^{3} -3y^{2}\frac{1}{y}+3y(\frac{1}{y})^{2}-(\frac{1}{y})^{3}$

$(y-\frac{1}{y})^{3}=y^{3}-(\frac{1}{y})^{3} -3(y-\frac{1}{y})$

$(3)^{3}=y^{3}-(\frac{1}{y})^{3} -3(3)$

$27=y^{3}-(\frac{1}{y})^{3} -9$

$y^{3}-(\frac{1}{y})^{3}=27+9 =33$

Hence, $y^{3}-(\frac{1}{y})^{3}=33$