Mathematics

If x³ = a + 1 and x + (b/x) = a , then x equals 

A)   [latex] \frac{a(b+1)}{a^{2} -b } [/latex]

B)   [latex] \frac{ab+1}{ a^{2} - b } [/latex]

C)   [latex] \frac{ab+a+1}{ a^{2}-b } [/latex]

D)   [latex] \frac{ab-a-1}{ a^{2}-b } [/latex]


Answers

b03172000

4 years ago Comment

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

Now we rewrite [latex]x^3[/latex]  using the above relation:

[latex]x^3=x\cdot x^2=x(ax-b)=ax^2-bx=a(ax-b)-bx=a^2x-bx-ab.[/latex]

But we know that [latex]x^3=a+1[/latex] , so we can write:

[latex]a^2x-bx-ab=a+1 \\ \\ x(a^2-b)=ab+a+1 \\ \\ \\ x=\dfrac{ab+a+1}{a^2-b}.[/latex]