8.6k views
3 votes
Let a = x2 + 4. Use a to find the solutions for the following equation:

(x2 + 4)2 + 32 = 12x2 + 48
Which of the following are solutions for x?​

User AndHeiberg
by
8.0k points

1 Answer

6 votes

The solutions for x are -2, 0, 2

Solution:

Given that,


\text { Let } a = x^2 + 4

Given equation is:


(x^2 + 4)^2 + 32 = 12x^2 + 48


(x^2 + 4)^2 + 32 = 12(x^2 + 4)


\text { Subtsitute } a = x^2 + 4 \text{ in above equation }


a^2 + 32 = 12a\\\\a^2 -12a + 32 = 0


\text{ Let us factorize the above equation }\\\\\text{ Splitting the middle term -12a as -4a - 8a we get, }


a^2 -4a - 8a + 32 = 0

Taking "a" as common term from first two terms and taking "-8" as common from last two terms


a(a-4)-8(a - 4) = 0


\text{Taking (a - 4) as common term, }\\\\(a - 4)(a - 8) = 0


\text{Equating to zero we get, }\\\\(a - 4) = 0 \text{ or } (a - 8) = 0\\\\a = 4 \text{ or } a = 8


\text{Now substitute the value of a = 8 and a = 4 in: }\\\\a = x^2 + 4


\text{ For a = 8: }\\\\a = x^2 + 4\\\\8 = x^2 + 4\\\\x^2 = 4\\\\x = \pm2\\\\x = +2 \text{ or } -2


\text{For a = 4: }\\\\a = x^2 + 4\\\\4 = x^2 + 4\\\\x = 0


\text{Thus solutions of } x \text{ are: }\\\\x = 0 \text{ or } x = 2 \text{ or } x = -2

User VikramV
by
9.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories