Algebra

Polynomial Factoring

Polynomial Factoring: Level 2 Challenges

         

a+b=7b+a=11 \large \sqrt a + b = 7 \\ \large \sqrt b + a = 11

If aa and bb are real numbers that satisfy the equation above, what is the value of aa and bb respectively?

Given that 6y2=20146y^2=2014, find the value of

9(y4+6y3+9y2)y2+6y+9.\frac{9\big(y^4+6y^3+9y^2\big)}{y^2+6y+9}.

a3+b3=2593080,  a+b=210,     ab= ?\large a^3 + b^3 = 2593080, \ \ a + b = 210, \ \ \ \ \ ab = \ ?

Given that a+b=1a+b=1 and a2+b2=2a^2+b^2=2, what is the value of a7+b7a^7+b^7?

If x25x1=0 x^2 - 5x - 1 = 0 , then find the value of x2+1x2. x^2 + \frac{1}{x^2}.

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