x²+1/x²=15 ; find x³-1/x³
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Abhi10001:
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a^3-b^3 = (a-b)(a^2+ab+b^2)
x^3-1/x^3 => (x-1/x)(x^2+x*1/x+1/x^2)=0
=> {(x^2-1)/x}{x^2+1/x^2+1} =0
=> {(x^2-1)/x}{15+1} =0
=> {(x^2-1/x}[16] =0
=> (x^2-1)/x=0
=> x^2-1=0
=> x^2=1
=> X=1
x^3-1/x^3 => (x-1/x)(x^2+x*1/x+1/x^2)=0
=> {(x^2-1)/x}{x^2+1/x^2+1} =0
=> {(x^2-1)/x}{15+1} =0
=> {(x^2-1/x}[16] =0
=> (x^2-1)/x=0
=> x^2-1=0
=> x^2=1
=> X=1
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