Find the value of $m$ if $5 m^{2} - 4 m - 2 = 0$

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Solution

Given equation is $5 m^{2} - 4 m - 2 = 0$

$m = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

$a = 5$

$b = - 4$

$c = - 2$

$m = \frac{+ 4 \pm \sqrt{4^{2} - 4 (5) (- 2)}}{2 (5)}$

$m = \frac{+ 4 \pm \sqrt{4^{2} - 4 (5) (- 2)}}{2 (5)}$

$m = \frac{+ 4 \pm \sqrt{16 + 40}}{2 (5)}$

$m = \frac{4 \pm \sqrt{56}}{10}$

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x^{2} - (5 m - 2) x + 4 m^{2} + 10 m + 25 = 0

m

m

5^{m} \div 5^{- 3} = 5^{5}

4^{m} = 64

8^{m - 3} = 1

(a^{3})^{m} = a^{9}

(5^{m})^{2} \times (25)^{3} \times 125^{2} = 1

2^{m} = (8)^{\frac{1}{3}} \div (2^{3})^{2 / 3}

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