perplexus.info :: Just Math : Given Quadratic, Find Cubic

Given Quadratic, Find Cubic (Posted on 2024-01-09)

Given that:
n² - 5n = 300
Find the value of :
n³ - 325n + 1503

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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solution

Comment 1 of 1

Reduce the degree of the polynomial by repeatedly substituting n^2 = 5n + 300

n(n^2) -325n + 1503

n(5n + 300) - 325n + 1503

5n^2 - 25n + 1503

5(5n + 300) - 25n + 1503

25n + 1500 - 25n + 1503

3003

Method 2: notice that

n^2 - 5n - 300 = (x + 15)(x-20) = 0

If this is zero, then x must be -15 or +20.

Plugging either into the cubic yields 3003.

Edited on January 9, 2024, 9:24 am

Posted by Larry on 2024-01-09 09:09:14

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