Given: 6m2+2m2=7 = gt; nbsp;6m4 + 2 = 7m2 = gt; 6m4 ndash; 7m2 + 2 = 0 Let m2 = y. Then, the equation can be written as: 6y2 ndash; 7y + 2 = 0 On sp ...

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Standard X

Mathematics

Elimination Method of Finding Solution of a Pair of Linear Equations

6 m 2+2 m 2=7

Question

$6 m^{2} + \frac{2}{m^{2}} = 7$

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Solution

Given:
$6 m^{2} + \frac{2}{m^{2}} = 7$
=> 6m⁴ + 2 = 7m²
=> 6m⁴ – 7m² + 2 = 0
Let m² = y.
Then, the equation can be written as:
6y² – 7y + 2 = 0
On splitting the middle term –7y as –3y – 4y, we get:
6y²– 3y – 4y + 2 = 0
=> 3y(2y – 1) –2(2y – 1) = 0
=> (2y – 1)(3y – 2) = 0
=> 2y – 1 = 0 or 3y – 2 = 0
=> y = $\frac{1}{2}$ or y = $\frac{2}{3}$
On substituting y = m², we get:
=> m² = $\frac{1}{2}$ or m² = $\frac{2}{3}$
=> m = ± $\frac{1}{\sqrt{2}}$ or m = ± $\sqrt{\frac{2}{3}}$
Thus, the solutions of the given equation are ± $\frac{1}{\sqrt{2}}$ , ± $\sqrt{\frac{2}{3}}$

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