if x=√5+2, then prove that x²+ 1/x²=18
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Answered by
4
x²+1/x²=18
taking L.H.S;
x²+1/x²=(√5+2)²+1/(√5+2)²
=(√5)²+2(√5)(2)+2²+1/(√5)²+2(√5)(2)+2²
=5+4√5+4+1/5+4√5+4
=10+4√5/9+4√5=19.938 which is not equal to 18
hence x²+1/x² is not equal to 18.
hope i helped u:)
taking L.H.S;
x²+1/x²=(√5+2)²+1/(√5+2)²
=(√5)²+2(√5)(2)+2²+1/(√5)²+2(√5)(2)+2²
=5+4√5+4+1/5+4√5+4
=10+4√5/9+4√5=19.938 which is not equal to 18
hence x²+1/x² is not equal to 18.
hope i helped u:)
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Answered by
3
x²=(√5+2)2=9+4√5
x²+ 1/x²=9+4√5+1/9+4√5
=((9+4√5)2+1)/ 9+4√5
=(81+80+72√5+1)/ 9+4√5
=162+72√5/9+4√5=18
x²+ 1/x²=9+4√5+1/9+4√5
=((9+4√5)2+1)/ 9+4√5
=(81+80+72√5+1)/ 9+4√5
=162+72√5/9+4√5=18
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