if (x-1/2x)=3 find the value of (x^4+1/16x^4)
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EXPLANATION.
⇒ (x - 1/2x) = 3.
As we know that,
Squaring both sides of the equation, we get.
⇒ (x - 1/2x)² = (3)².
⇒ (x² + 1/4x² - 2(x)(1/2x)) = 9.
⇒ (x² + 1/4x² - 1) = 9.
⇒ (x² + 1/4x²) = 9 + 1.
⇒ (x² + 1/4x²) = 10.
Again squaring on both sides of the equation, we get.
⇒ (x² + 1/4x²)² = (10)².
⇒ x⁴ + 1/16x⁴ + 2(x²)(1/4x²) = 100.
⇒ x⁴ + 1/16x⁴ + 2x²/4x² = 100.
⇒ x⁴ + 1/16x⁴ + 1/2 = 100.
⇒ x⁴ + 1/16x⁴ = 100 - 1/2.
⇒ x⁴ + 1/16x⁴ = 200 - 1/2.
⇒ x⁴ + 1/16x⁴ = 199/2.
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