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If x+1/x = 5 then!!!!!!!!!!!!!!!!!!!!!

+2 votes

(x^4+1/x^2)/x^2-3x+1 = what?

asked Feb 15, 2013 in ALGEBRA 1 by andrew Scholar

1 Answer

+2 votes

Presumed [x+(1/x)]=5 then [x4+(1/x)4]/[x2 - 3x + 1]=?

[x+(1/x)] = 5

Apply square each side.

[x+(1/x)]2 = 52

Mathematical formula: (a + b)2 = a2+ 2ab + b2

x2 + 2x(1/x)+(1/x)2 = 25

x2 + 2 + (1/x)2 = 25

Subtract 2 from each side.

x2 + (1/x)2 = 23.

Again apply square each side.

[x2 + (1/x)2]2 = 232

x4 + 2x2(1/x2)+1/x4 = 529

x4 + 2 + (1/x)4 = 529

Subtract 2 from each side.

x4 + (1/x)4 = 527----------->(1)

Take x+(1/x) = 5

Multiply each side by x.

x2 + 1 = 5x.

Subtract 3x from each side.

x2 + 1 - 3x = 2x----------(2)

Divide equation (1) and equation (2).

Therefore [x4+(1/x)4]/[x2 - 3x + 1] = 527/(2x) = 263.5/x.

answered Feb 15, 2013 by richardson Scholar

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