Question

the sum of four times a number and three times its reciprocal is 7 find the number

Answer 1

Here values are x = 1,
$\frac{3}{4}$

Answer 2

Given: The sum of four times a number and three times its reciprocal is 7

To Find: The number

Solution:

Let the number be a

So, the reciprocal of the number will be 1/a

Four times the number will be 4a

Three times the reciprocal of the number will be 3/a

Four times the number + Three times the reciprocal of the number = 7 (Given)

4a + $\frac{3}{a}$ = 7

Taking a as common denominator

$\frac{4a^{2} + 3 }{a}$ = 7

On cross multiplying

4a² + 3 = 7a

4a² - 7a + 3 = 0

4a² - 4a - 3a + 3 = 0

4a( a - 1) -3(a - 1) = 0

(4a - 3) (a- 1) = 0

a = 3/4 or a = 1

Therefore, the number can be 3/4 or 1.