Writing algebraic expressions for: A number decreased by 5 is 12
1 answer:
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Answer:
= 1
Step-by-step explanation:
<h3>Given</h3>- The value of the expression
<u>Let's rewrite the given as:</u>
- <u />
<u>Let the value is m and the expressions under 3rd roots are a and b, then we have </u>
- a = 3√21 + 8, b = 3√21 - 8
- m = ∛a - ∛b
<u>Cube the both sides:</u>
- m³ = (∛a - ∛b)³
- m³ = a - b - 3
+ 3
<u>Simplify in bits:</u>
- a - b = 3√21 + 8 - 3√21 + 8 = 16
- ab = (3√21 + 8)(3√21 - 8) = 9*21 - 64 = 125
- ∛ab = ∛125 = 5
<u>So the expression becomes:</u>
- m³ = 16 - 3
- m³ = 16 - 15∛a + 15∛b
- m³ = 16 - 15(∛a - ∛b)
- m³ = 16 - 15m
<u>Solve for m:</u>
- m³ + 15m - 16 = 0
- m³ - 1 + 15m - 15 = 0
- (m - 1)(m² + m + 1) + 15(m - 1) = 0
- (m - 1)(m² + m + 16) = 0
- m - 1 = 0, m² + m + 16 = 0
- m = 1 is the only real root, the quadratic equation has no real roots
The answer is 1