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3 years ago

Simplify the expression (x^3/x^4)^2

Mathematics

1 answer:

DedPeter [7]3 years ago

7 0

Answer:

Step-by-step explanation:

(x^3/x^4)^2

=(x^3×x^{-4})^2

=(x^{3-4})^2

=(x^{-1})^2

=1/x²

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Use the identity (x2+y2)2=(x2−y2)2+(2xy)2 to determine the sum of the squares of two numbers if the difference of the squares of

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Answer:

The sum of the squares of two numbers whose difference of the squares of the numbers is 5 and the product of the numbers is 6 is <u>169</u>

Step-by-step explanation:

Given : the difference of the squares of the numbers is 5 and the product of the numbers is 6.

We have to find the sum of the squares of two numbers whose difference and product is given using given identity,

$(x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2$

Since, given the difference of the squares of the numbers is 5 that is $(x^2-y^2)^2=5$

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Using identity, we have,

$(x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2$

Substitute, we have,

$(x^2+y^2)^2=(5)^2+(2(6))^2$

Simplify, we have,

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