Question

Let p=x^2-2p=x 2 −2p, equals, x, squared, minus, 2. Which equation is equivalent to (x^2-2)^2+18=9x^2-18(x 2 −2) 2 +18=9x 2 −18left parenthesis, x, squared, minus, 2, right parenthesis, squared, plus, 18, equals, 9, x, squared, minus, 18 in terms of ppp ?

Answer 1

Question:

Let $p=x^2-2$ .

Which equation is equivalent to in terms of p ?

Answer:

$p^2+18=9p$ or $p^2+18 - 9p = 0$

Step-by-step explanation:

Given

$p=x^2-2$ .

Required

Find the equation equivalent to $(x^2-2)^2+18=9x^2-18$

To get the equation equivalent to the given expression, we simply simplify $(x^2-2)^2+18=9x^2-18$ and solve in terms of p

$(x^2-2)^2+18=9x^2-18$

Factorize expression on the right hand side

$(x^2-2)^2+18=9(x^2-2)$

Substitute $x^2 - 2$ for p

$(x^2-2)^2+18=9(x^2-2)$ becomes

$p^2+18=9p$

Hence, equation $p^2+18=9p$ is equivalent to $(x^2-2)^2+18=9x^2-18$

Solving further to get the value of p

$p^2+18=9p$

Subtract 9p from both sides

$p^2+18 - 9p = 9p - 9p$

$p^2+18 - 9p = 0$

Rearrange

$p^2 - 9p +18 = 0$

Factorize

$p^2 - 6p - 3p +18 = 0$

$p(p - 6) - 3(p -6) = 0$

$(p - 3)(p -6) = 0$

p - 3 = 0 or p - 6 = 0

p = 3 or p = 6