If x+1=√3+√2 then x^2+1/x^2=?
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may be it will not help u as much..regards
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here is the answer
= x^2+1/x^2
=(x^4+1)1/x^2-----------eq 1
x^2= ((√3+√2)-1)^2
x^2 = (√3+√2)^2+1-2 (√3+√2)
x^2=3+2+2√6+1-2√3-2√2
x^2=6+2(√6-√3-√2)
by putting this value in equation 1
=([6+2(√6-√3-√2)]^2+1)1/ 6+2(√6-√3-√2)
=[36+4(√6-√3-√2)^2+24 (√6-√3-√2) +1)] 1/ 6+2(√6-√3-√2
=[36 + 4 (6- 3- 2- 2√6 -2(√6)(√3+√2)] +24√6-24√3- 24√2+1)]1/ 6+2(√6-√3-√2)
=[36+24-12-8+1-8√6-2√18-2√12+ 24√6 - 24√3 - 24√2] 1/ 6+2(√6-√3-√2)
you can solve further
= x^2+1/x^2
=(x^4+1)1/x^2-----------eq 1
x^2= ((√3+√2)-1)^2
x^2 = (√3+√2)^2+1-2 (√3+√2)
x^2=3+2+2√6+1-2√3-2√2
x^2=6+2(√6-√3-√2)
by putting this value in equation 1
=([6+2(√6-√3-√2)]^2+1)1/ 6+2(√6-√3-√2)
=[36+4(√6-√3-√2)^2+24 (√6-√3-√2) +1)] 1/ 6+2(√6-√3-√2
=[36 + 4 (6- 3- 2- 2√6 -2(√6)(√3+√2)] +24√6-24√3- 24√2+1)]1/ 6+2(√6-√3-√2)
=[36+24-12-8+1-8√6-2√18-2√12+ 24√6 - 24√3 - 24√2] 1/ 6+2(√6-√3-√2)
you can solve further
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