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zlopas [31]
3 years ago
9

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 −18l

eft parenthesis, x, squared, minus, 2, right parenthesis, squared, plus, 18, equals, 9, x, squared, minus, 18 in terms of ppp ?
Mathematics
1 answer:
masya89 [10]3 years ago
5 0

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

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