Question

[tex]650=\frac{2n^{^3}+3n^{2}+n}{6}

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650=(2n³+3n²+n)/6

Answer 1

650 = [2 n³ + 3 n² + n]/6

Mnożymy obie strony równania prze 6

3 900 = 2 n³ + 3 n² + n

Odgaduję, że n = 12 , bo

2 *12³ + 3*12² + 12 = 2*1728 + 3*144 + 12 = 3456 + 432 + 12 = 3 900

Odp. n = 12

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II sposób:

2 n³ + 3 n² + n = 3 900

n(2n² + 3n + 1) = 3 900

Δ = 9 - 4*2*1 = 9 - 8 = 1

n1 = [ -3 -1]/4 = -1

n2 = [ -3 +1]/4 = -1/2

zatem

2n² +3n +1 = 2(n +1)(n +1/2) = (n +1)(2n + 1)

oraz

2 n³ + 3n² + n = n(n +1)(2n +1)

n( n +1)(2n +1) = 3 900 = (2*2*3]*13*[5*5] = 12*13*25

zatem

n = 12

n +1 = 13

2n +1 = 25

Odp. n = 12

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