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Komok [63]
3 years ago
8

Is 2a * b = a^2 + b^2 true or false

Mathematics
1 answer:
alisha [4.7K]3 years ago
5 0

First step of the equation is to simplify the equation 2a • b = a2 + b2 into 2 ab = a2 + b2. This cannot be factored anymore although. when we try to substitute a with 5 and b with 2, the answer in the right hand side of the equation is -9. hence the answer to this problem is false. we can try another values to verify.


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Answer:

n>3

Step-by-step explanation:

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2 years ago
If x = (√2 + 1)^-1/3 then the value of x^3 + 1/x^3 is​
Shtirlitz [24]

Step-by-step explanation:

<u>Given</u><u>:</u> x = {√(2) + 1}^(-1/3)

<u>Asked</u><u>:</u> x³+(1/x³) = ?

<u>Solution</u><u>:</u>

We have, x = {√(2) + 1}^(-1/3)

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⇛(x)³ = [1{/√(2) + 1}^(1/3)]³

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⇛(x)³ = [(1)³/{√(2) + 1}^(1*3/3)]

⇛(x)³ = [(1)³/{√(2) + 1}^(3/3)]

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Here, we see that on RHS, the denominator is √(2)+1. We know that the rationalising factor of √(a)+b = √(a)-b. Therefore, the rationalising factor of √(2)+1 = √(2) - 1. On rationalising the denominator them

⇛x³ = [1/{√(2) + 1}] * [{√(2) - 1}/{√(2) - 1}]

⇛x³ = [1{√(2) + 1}/{√(2) + 1}{√(2) - 1}]

Multiply the numerator with number outside of the bracket with numbers on the bracket.

⇛x³ = [{√(2) + 1}/{√(2) + 1}{√(2) - 1}]

Now, Comparing the denominator on RHS with (a+b)(a-b), we get

  • a = √2
  • b = 1

Using identity (a+b)(a-b) = a² - b², we get

⇛x³ = [{√(2) - 1}/{√(2)² - (1)²}]

⇛x³ = [{√(2) - 1}/{√(2*2) - (1*1)}]

⇛x³ = [{√(2) - 1}/(2-1)]

⇛x³ = [{√(2) - 1}/1]

Therefore, x³ = √(2) - 1 → → →Eqn(1)

Now, 1/x³ = [1/{√(2) - 1]

⇛1/x³ = [1/{√(2) - 1] * [{√(2) + 1}/{√(2) + 1}]

⇛1/x³ = [1{√(2) + 1}/{√(2) - 1}{√(2) + 1}]

⇛1/x³ = {√(2) + 1}/[{√(2) - 1}{√(2) + 1}]

⇛1/x³ = [{√(2) + 1}/{√(2)² - (1)²}]

⇛1/x³ = [{√(2) + 1}/{√(2*2) - (1*1)}]

⇛1/x³ = [{√(2) + 1}/(2-1)]

⇛1/x³ = [{√(2) + 1}/1]

Therefore, 1/x³ = √(2) + 1 → → →Eqn(2)

On adding equation (1) and equation (2), we get

x³ + (1/x³) = √(2) -1 + √(2) + 1

Cancel out -1 and 1 on RHS.

⇛x³ + (1/x³) = √(2) + √(2)

⇛x³ + (1/x³) = 2

Therefore, x³ + (1/x³) = 2

<u>Answer</u><u>:</u> Hence, the required value of x³ + (1/x³) is 2.

Please let me know if you have any other questions.

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Step-by-step explanation:

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