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vesna_86 [32]
3 years ago
9

What is the factored form x^3 - 1 ?

Mathematics
1 answer:
amid [387]3 years ago
7 0

Answer: x^3 - 1 = (x - 1)(x^2 + x + 1)

Explanation:

This is a type of factorizing called the sum or difference of 2 cubes:

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

The sum of the cubes is factored as:

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

In this case, we have: x^3 - 1 so follow the rule above.

x^3 - 1 = (x - 1)(x^2 + x + 1)

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If x=3+root8 and y =3- root 8 find 1/x^2+1/y^2
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Answer:

34

Step-by-step explanation:

x=3+√8

y =3-√8

now,

1/x^2+1/y^2

=1/(3+√8)² + 1/(3-√8)²

= [(3-√8)²+(3+√8)²] / (3+√8)²(3-√8)²            [L.C.M  = (3+√8)²(3-√8)² ]

=[(3-√8+3+√8)²-2(3-√8)(3+√8) ] / [(3+√8)(3-√8)]²  

=[6²-2.(3²-√8² )] / (3²-√8²)²                 [ a²+ b²=(a+b)²-2ab]

=[36-2(9-8) ]/ (9-8)²

=[36-2.1] / 1²

=34

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