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(#M40154869) SSC Numerical Ability question Algebra Keep an EYE

If X = 2 - 2^(2/3) + 2^(1/3) , X3-6X2+18X-18 is

Asked In SSC Hari (9 years ago)

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Rishu  (9 years ago)

X=2-2^(2/3)+2^(1/3)
X-2=2^(1/3)-2^(2/3)....(1)

X^3-6X^2+18X-18=[((X-2)^3)-(X^3-8-6X^2+12X)+(X^3-6X^2+18X-18)].....[Since (X-2)^3=X^3-8-6X^2+12X]
X^3-6X^2+18X-18=(X-2)^3+6X-10.....(2)

(X-2)^3=(2^(1/3)-2^(2/3))^3
(X-2)^3=(2^(1/3))^3-(2^(2/3))^3-3*(2^(1/3))*(2^(2/3))*(2^(1/3)-2^(2/3))
(X-2)^3=2-4-6*(2^(1/3)-2^(2/3))
(X-2)^3=2-4-6(X-2).....From(1)
(X-2)^3=2-4-6X+12
(X-2)^3=10-6X
(X-2)^3+6X-10=0
X3-6X2+18X-18=0.....From(2)

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Rishu  (9 years ago)

X=2-2^(2/3)+2^(1/3)
X-2=2^(1/3)-2^(2/3)..........................................................................................................................................(1)

X^3-6X^2+18X-18=[((X-2)^3)-(X^3-8-6X^2+12X)+(X^3-6X^2+18X-18)]...........[Since (X-2)^3=X^3-8-6X^2+12X]
X^3-6X^2+18X-18=(X-2)^3+6X-10....................................................................................................................(2)

(X-2)^3=(2^(1/3)-2^(2/3))^3
(X-2)^3=(2^(1/3))^3-(2^(2/3))^3-3*(2^(1/3))*(2^(2/3))*(2^(1/3)-2^(2/3))
(X-2)^3=2-4-6*(2^(1/3)-2^(2/3))
(X-2)^3=2-4-6(X-2)...................................................................................................................................From(1)
(X-2)^3=2-4-6X+12
(X-2)^3=10-6X
(X-2)^3+6X-10=0
X3-6X2+18X-18=0....................................................................................................................................From(2)

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