Question

if x= root 3+ root 2 find the value of x4 +1/x4​

Answer 1

x=√3+√2

so, 1/x= √3-√2

(√3+√2)²(√3+√2)²+(√3-√2)²(√3-√2)²

(3+2+2√6)(3+2+2√6)+(3+2-2√6)(3+2-2√6)

(5+2√6)²+(5-2√6)²

25+24+25-24

50 is your answer

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Answer 2

Answer:

$x = \sqrt{3} + \sqrt{2} \\ \\ \frac{1}{x} = \frac{1}{ \sqrt{3} + \sqrt{2} } = \sqrt{3} - \sqrt{2}$

NOW X+1/X:

$\sqrt{3} + \sqrt{2} + \sqrt{3} - \sqrt{2} \\ \\ = 2 \sqrt{3} \\ \\ ({ {2 \sqrt{3} }^{2} })^{2} - 2 \\ \\ = {12}^{2} - 2 = 144 - 2 = 142$