Question 156591
1.x^4=5x^2
x^4 - 5x^2 = 
x^2 (x^2 - 5) = 0
x^2 (x-sqrt(5))(x+sqrt(5)) = 0
x = 0 or x = sqrt(5) or x = -sqrt(5)
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2.x^4+18x^3+8x+144=0
x^3(x+18) + 8(x+18) = 0
(x+18)(x^3+8) = 0
(x+18)(x+2)(x^2-2x+4) = 0
x = -18 or x = -2 or x^2-2x+4 =0
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Use the quadratic formula on x^2-2x+4
x = [2 +- sqrt(4 - 4*1*4)]/2
x = [2 +- sqrt(-12)]/2
x = [1 +- isqrt(3)]
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3.x^3+19x^2-7x-133=0
x^2(x + 19) -7(x+19) = 0 
(x+19)(x^2-7) = 0 
(x+19)(x-sqrt(7))(x+sqrt(7)) = 0
x = -19 or x=sqrt(7) or x=-sqrt(7)
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4.x^6-13x^5-7x=-91
x^6 - 13x^5 -7x + 91 = 0
x^5(x-13) - 7(x-13) = 0
(x-13)(x^5-7) = 0
x = 13 and x = 7^(1/5)
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Cheers,
Stan H.