Question 4

Determine the value of $$(y-\frac{1}{y})^2$$ when $$y^4+\frac{1}{y^4}=34$$

Solution

Given : $$y^4+\frac{1}{y^4}=34$$

=> $$(y^2+\frac{1}{y^2})^2-2(y^2)(\frac{1}{y^2})=34$$

=> $$(y^2+\frac{1}{y^2})^2=34+2=36$$

=> $$y^2+\frac{1}{y^2}=\sqrt{36}=6$$

=> $$(y-\frac{1}{y})^2+2(y)(\frac{1}{y})=6$$

=> $$(y-\frac{1}{y})^2=6-2=4$$

=> Ans - (D)

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