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Algebra Level 3

If $x^2=7x+5$ , then we can write $x^3$ as $ax+b$ . Find the value of $a+b$ .

1 solution

Brian Charlesworth
Nov 5, 2015

Multiplying the given equation through by $x$ gives us that

$x^{3} = 7x^{2} + 5x = 7(7x + 5) + 5x = 54x + 35 \Longrightarrow a + b = 54 + 35 = \boxed{89}.$

That is very difficult to follow. Clarification on your solution would be greatly appreciated.

Peter Michael - 5 years, 7 months ago

Sorry, I combined a few steps for sake of brevity. Given that $x^{2} = 7x + 5,$ we then have that

$x*x^{2} = x*(7x + 5) \Longrightarrow x^{3} = 7x^{2} + 5x.$

Now substitute $x^{2} = 7x + 5$ to find that

$x^{3} = 7*(7x + 5) + 5x \Longrightarrow x^{3} = 49x + 35 + 5x = 54x + 35,$

from which we have that $a = 54$ and $b = 35.$

Brian Charlesworth - 5 years, 7 months ago