Mathematics

# If x³ = a + 1 and x + (b/x) = a , then x equals  A)   $\frac{a(b+1)}{a^{2} -b }$ B)   $\frac{ab+1}{ a^{2} - b }$ C)   $\frac{ab+a+1}{ a^{2}-b }$ D)   $\frac{ab-a-1}{ a^{2}-b }$

#### b03172000

4 years ago

We rewrite the second equation:
$\dfrac{x^2+b}{x}=a\ \ \ \ \ \Rightarrow \ \ \ \ \ x^2=ax-b.$

Now we rewrite $x^3$  using the above relation:

$x^3=x\cdot x^2=x(ax-b)=ax^2-bx=a(ax-b)-bx=a^2x-bx-ab.$

But we know that $x^3=a+1$ , so we can write:

$a^2x-bx-ab=a+1 \\ \\ x(a^2-b)=ab+a+1 \\ \\ \\ x=\dfrac{ab+a+1}{a^2-b}.$