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ratelena [41]
3 years ago
7

What substitution should be used to rewrite 16(x3 + 1)2 – 22(x3 + 1) – 3 = 0 as a quadratic equation?

Mathematics
2 answers:
Vesna [10]3 years ago
7 0

Answer:

  z = x^3 +1

Step-by-step explanation:

Noting the squared term, it makes sense to substitute for that term:

  z = x^3 +1

gives ...

  16z^2 -22z -3 = 0 . . . . the quadratic you want

_____

<em>Solutions derived from that substitution</em>

Factoring gives ...

  16z^2 -24z +2z -3 = 0

  8z(2z -3) +1(2z -3) = 0

  (8z +1)(2z -3) = 0

  z = -1/8  or  3/2

Then we can find x:

  x^3 +1 = -1/8

  x^3 = -9/8 . . . . . subtract 1

  x = (-1/2)∛9 . . . . . one of the real solutions

__

  x^3 +1 = 3/2

  x^3 = 1/2 = 4/8 . . . . . . subtract 1

  x = (1/2)∛4 . . . . . . the other real solution

The complex solutions will be the two complex cube roots of -9/8 and the two complex cube roots of 1/2.

anastassius [24]3 years ago
5 0

Answer:

x^3 +1

Step-by-step explanation:

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3 0
3 years ago
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Answer fast but correctly​
olasank [31]

{m}^{2}  - n \\ Given, \:  \: m = 3 \:  \: n = 2, then, \\ \:  \:  {(3)}^{2}  - 2 \\  = 9 - 2 \\  = 7

<u>Answer</u><u>:</u>

<u>a.</u><u> </u><u>7</u>

Hope you could understand.

If you have any query, feel free to ask.

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Answer:

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Step-by-step explanation:

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