GIVEN:x4 + x-4 = 194Identity used:(a + b)2 = a2 + b2 + 2abCalculation:x4 + x-4 = 194Adding 2 on both sidesx4 + x-4 + 2 = 194 + 2⇒ (x2 + 1/x2)2 = 196 = 142⇒ x2 + 1/x2 = 14Again ADDING 2 on both sidesx2 + 1/x2 + 2 = 14 + 2⇒ (x + 1/x)2 = 16 = 42 ∴ x + 1/x is 4 "> GIVEN:x4 + x-4 = 194Identity used:(a + b)2 = a2 + b2 + 2abCalculation:x4 + x-4 = 194Adding 2 on both sidesx4 + x-4 + 2 = 194 + 2⇒ (x2 + 1/x2)2 = 196 = 142⇒ x2 + 1/x2 = 14Again ADDING 2 on both sidesx2 + 1/x2 + 2 = 14 + 2⇒ (x + 1/x)2 = 16 = 42 ∴ x + 1/x is 4 ">
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If x4 + x-4 = 194, x > 0, then the value of \(x+\dfrac{1}{x}\) is:

General Aptitude Algebra in General Aptitude . 3 months ago

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GIVEN:x4 + x-4 = 194Identity used:(a + b)2 = a2 + b2 + 2abCalculation:x4 + x-4 = 194Adding 2 on both sidesx4 + x-4 + 2 = 194 + 2⇒ (x2 + 1/x2)2 = 196 = 142⇒ x2 + 1/x2 = 14Again ADDING 2 on both sidesx2 + 1/x2 + 2 = 14 + 2⇒ (x + 1/x)2 = 16 = 42 ∴ x + 1/x is 4
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