Question

if X= 4- ✓15 find the value of (X+1/X)²- (x-1/x)²

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Answer 1

Answer:

Step-by-step explanation:

Answer 2

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$x = 4 - \sqrt{15} \\ \frac{1}{x} = \frac{1}{4 - \sqrt{15} } \\ \frac{1}{x} = \frac{1}{4 - \sqrt{15} } \times \frac{4 + \sqrt{15} }{4 + \sqrt{15} } \\ = \frac{4 + \sqrt{15} }{16 - 15} \\ = 4 + \sqrt{15} \\ x + \frac{1}{x} = 4 - \sqrt{15 } + 4 + \sqrt{15} = 8 \\ ( {x + \frac{1}{x} })^{2} = {8}^{2} = 64 \\ x - \frac{1}{x} = 4 - \sqrt{15} - 4 - \sqrt{15} = - 2 \sqrt{15} \\ ( {x - \frac{1}{x} })^{2} = ( - 2 \sqrt{15} ) ^{2} = 60 \\ \\ \therefore \: \: \: ( {x + \frac{1}{x} })^{2} - ( {x - \frac{1}{x} })^{2} = 64 - 60 = 4$