Find your X

Algebra Level 2

S o l v e f o r x x 4 − 10 x 2 + 9 x 3 + 3 x 2 − x − 3 = 5 7 \qquad \qquad Solve\quad for\quad x\\ \\ \frac { { x }^{ 4 }\quad -\quad 10{ x }^{ 2 }\quad +\quad 9 }{ { x }^{ 3 }\quad +\quad { 3x }^{ 2 }\quad -\quad x\quad -\quad 3 } \quad =\quad \frac { 5 }{ 7 }

Write your answers as an improper fraction a b \frac{a}{b} then a + b


The answer is 33.

Angela Fajardo by Angela Fajardo , 19, Philippines

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2 solutions

Erza Scarlet
Apr 21, 2015

factoring ( x − 1 ) ( x + 1 ) ( x − 3 ) ( x + 3 ) ( x − 1 ) ( x + 3 ) ( x + 1 ) \frac{(x-1)(x+1)(x-3)(x+3)}{(x-1)(x+3)(x+1)}

cancelling out

( x − 3 ) = 5 7 (x-3)=\frac{5}{7}

x = 26 7 x=\frac{26}{7}

= 33 =\boxed{33}

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Also Correct. Very Nice solution.

Angela Fajardo - 6 years, 1 month ago

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Thank you :)

Erza Scarlet - 6 years, 1 month ago
Ruslan Abdulgani
Apr 15, 2015

(x^2 – 9)( x^2 – 1)/( x^2 – 1)(x + 3) = x – 3 = 5/7, x=3 5/7 = 26/7, a+b=33

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Very good, just like how I did it but I factored x^2 -9 to (x-3)(x+3) to better see the x-3 there. Very Nice.

Angela Fajardo - 6 years, 2 months ago

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