If $m + 2 n = 5$ , express $5 m^{2} - 3 n - 8$ in terms of $n .$

20 n^{2} - 103 n + 117

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6 n^{2} - 230 n + 13

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12 n^{2} - 91 n + 13

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10 n^{2} - 130 n + 117

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Solution

The correct option is A $20 n^{2} - 103 n + 117$
$m + 2 n = 5 \Rightarrow m = 5 - 2 n$
On substituting $m = 5 - 2 n$ in $5 m^{2} - 3 n - 8$ , we get
$5 m^{2} - 3 n - 8 = 5 (5 - 2 n)^{2} - 3 n - 8$
$= 5 (25 + 4 n^{2} - 20 n) - 3 n - 8$
$= 125 + 20 n^{2} - 100 n - 3 n - 8$
$= 20 n^{2} - 103 n + 117$

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Similar questions

m + 2 n = 5

5 m^{2} - 3 n - 8

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If HCF of 65 and 117 can be expressed in the form 65m+117n, find the value of m and n.

2 {sin}^{- 1} \frac{3}{5} - {tan}^{- 1} \frac{17}{31} = \frac{π}{4}

2 {sin}^{- 1} (\frac{3}{5}) - {tan}^{- 1} (\frac{17}{31}) = \frac{π}{4}

Fond the HCF of 65 and 117 and express it in the form 65n + 117n.

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