Solve this with step by step and explanation. Pls by request
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We have,
x+\dfrac{1}{x}=4 ....(1)
To find, x^2+\dfrac{1}{x^2}=?
Squaring (1) in both sides, we get
(x+\dfrac{1}{x})^{2}=4^{2}
⇒ x^2+\dfrac{1}{x^2}+2.x.\dfrac{1}{x} =16
⇒ x^2+\dfrac{1}{x^2}+2 =16
⇒x^2+\dfrac{1}{x^2}=16-2=14
∴ x^2+\dfrac{1}{x^2}=14
Hence, x^2+\dfrac{1}{x^2}=14
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