Step-by-step explanation:
x² - 2 = 2^(2/3) + 2^(-2/3)
x² = 2^(2/3) + 2 + 2^(-2/3)
x² = (2^(1/3))² + 2 × 2^(1/3) × 2^(-1/3) +
(2^(-1/3))² (It is in the form of a²+2ab+b²)
x² = (2^(1/3) + 2^(-1/3))²
x = 2^(1/3) + 2^(-1/3)
Here is one way to solve for x.
Step 1) 2x^2-7=9
Step 2) 2x^2-7+7=9+7
Step 3) 2x^2=16
Step 4) (2x^2)/2=16/2
Step 5) x^2=8
Step 6) sqrt(x^2)=sqrt(8)
Step 7) |x|=sqrt(8)
Step 8) x=sqrt(8) or x=-sqrt(8)
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Below are explanations/reasons to each of the steps above.
Step 1) Original equation
Step 2) Add 7 to both sides
Step 3) Combine like terms
Step 4) Divide both sides by 2
Step 5) Simplify
Step 6) Apply the square root to both sides. The notation "sqrt" is shorthand for "square root"
Step 7) Use the rule that sqrt(x^2) = |x| for all real numbers x
Step 8) Use the rule that if |x| = k then x = k or x = -k for some fixed number k.
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The two solutions are
x = sqrt(8) or x = -sqrt(8)
The answer is 60% but you can make it higher if your teacher let's you correct it.
Can you tell me by how many dollars has the price risen
