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Solve equation after making an appropriate substitution:

X4 - 19x2+48=0 

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Mark M. | Math Tutor--High School/College levelsMath Tutor--High School/College levels
4.9 4.9 (787 lesson ratings) (787)
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x4 - 19x2 + 48 = 0
 
(x2)2 - 19(x2) + 48 = 0
 
Let u = x2
 
Then, u2 - 19u + 48 = 0
 
        (u - 16)(u - 3) = 0
 
u = 16 or u = 3
 
So, x2 = 16 or x= 3
 
x = ±√16 or ±√3
 
x = 4, -4, √3, -√3
Michael H. | 15 years of experience helping you succeed15 years of experience helping you succe...
4.9 4.9 (326 lesson ratings) (326)
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This is really similar to your standard binomial equation: ax2+bx+c.  We treat it similarly. and start by factoring 
 
Factor:
(x2-16)(x2-3)
 
We ask ourselves: can I factor THESE any further.  Yes I can, so set each equation to 0 and solve again
x2-16 = (x+4)(x-4); x = ±4
x2-3 = (x+√3)(x-√3); x = ±√3
 
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