Question

7x-5/2x=3 solve the equations​

Answer 1

Answer:

7x - 5 / 2x = 3

7x - 5 = 6x

7x - 6x = 5

x = 5.

Answer 2

Answer:

$\frac{3\frac{+}{} \ 2\sqrt{11} }{7}$ is the required value of x.

Step-by-step explanation:

Explanation:

Given that, $7x - \frac{5}{2x} = 3$

This can be written as, $\frac{7x}{1} - \frac{5}{2x}$ = 3

LCM of 1 and 2x is 2x.

⇒$\frac{7x^2 -5}{2x}$ = 3

⇒$7x^2 -5 = 6x$

⇒$7x^2 -6x -5 = 0$

Step 1:

We have, $7x^2 -6x -5 = 0$

• Discriminant - The section of the quadratic formula following the square root symbol, $b^2 - 4ac$ , is the discriminant.

• If there are two solutions, one solution, or none at all, the discriminant informs us.

Formula, D = $\frac{-b \frac{+}{}\sqrt{b^2 - 4ac} }{2a}$

From the question we have, b = -6, a = 7 and c = -5

Now, from the formula, $b^2 -4ac$

⇒ $(-6)^2 - 4 (7)(-5)$ = 36 + 28 (5)

⇒ 36 + 140 = 176.

On putting the values in the discriminant formula,

⇒ x = $\frac{-(-6)\frac{+}{} \sqrt{176} }{2(7)}$ = $\frac{6\frac{+}{} \sqrt{176} }{14}$

⇒ x = $\frac{6\frac{+}{} \ 4\sqrt{11} }{14}$ = $\frac{3\frac{+}{} \ 2\sqrt{11} }{7}$

Here we can see that on solving $7x - \frac{5}{2x} = 3$ we get x = $\frac{3\frac{+}{} \ 2\sqrt{11} }{7}$.

Final answer:

Hence, $\frac{3\frac{+}{} \ 2\sqrt{11} }{7}$ is the required value of x.

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