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Bogdan [553]
3 years ago
13

Solve for x. 4x−3+2x2−9=1x+3 −173 −5 133 193

Mathematics
1 answer:
AnnyKZ [126]3 years ago
3 0

Answer:

-1711005

Step-by-step explanation:

using BODMAS that implies you multiplication(M),before addition(A), then substraction(S) which comes last.

use the above rule to get the variable without letter only.

so ( 2*2)+(-3)=1

then 1-9=8, this part is for the left hand side which gives us 4x-8.

then the right hañd side 3-173-5133193 not including the variable with the letter x.now we have:1x-5133023.

so now

4x-8=1x-5133023

collect like terms

4x-1x=-5133023+8

3x=-5133015

divide both side by 3

x= -1711005

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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>

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Cubing on both sides, then

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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

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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}]

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⇛1/x³ = [{√(2) + 1}/{√(2)² - (1)²}]

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⇛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

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Cancel out -1 and 1 on RHS.

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⇛x³ + (1/x³) = 2

Therefore, x³ + (1/x³) = 2

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

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