Question

M+2/3=1/4m-1


what the formula used to find the value of m?​

Answer 1

The value of m is
`(-5+√(34))/(6) \text { or } (-5-√(34))/(6)` by using quadratic formula

Solution:

Given, expression is
`m+(2)/(3)=(1)/(4 m)-1`

Now, we have to solve the above given expression.

`\text { Now, } \mathrm{m}+(2)/(3)=(1)/(4 m)-1`

By multiplying the equation with m, we get

`\begin{array}{l}{m^(2)+(2)/(3) m+m=(1)/(4)} \\\\ {m^(2)+m\left((2)/(3)+1\right)=(1)/(4)} \\\\ {m^(2)+(5)/(3) m=(1)/(4)}\end{array}`

`\begin{array}{l}{12 m^(2)+20 m=3} \\ {12 m^(2)+20 m-3=0}\end{array}`

Now, let us use quadratic formula

`\frac{-b \pm \sqrt{b^(2)-4 a c}}{2 a}`

Here in our problem, a = 12, b = 20, c = -3

`\begin{array}{l}{m=\frac{-20 \pm \sqrt{20^(2)-4 * 12 *(-3)}}{2 * 12}} \\\\ {=(-20 \pm √(400+144))/(24)} \\\\ {=(-20 \pm √(544))/(24)} \\\\ {=(-20 \pm 4 √(34))/(24)=(-5 \pm √(34))/(6)} \\\\ {=(-5+√(34))/(6) \text { or } (-5-√(34))/(6)}\end{array}`

Hence the value of m is
`(-5+√(34))/(6) \text { or } (-5-√(34))/(6)` by using quadratic formula