Question

The sum of four times a number and three times it's reciprocal is 7.Find the number.

Answer 1

$\huge \bold\red{ < ram \: ram \:ji > }$

$\huge \boxed{ = ans. = > }$

Let the number be x,

Reciprocal of x = 1/x

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Four times of x = 4x

3 times its reciprocal = 3/x

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ATQ,

4x + 3/x = 7

4x² + 3 = 7x

4x² - 7x + 3 = 0

4x² - (4 + 3)x + 3 = 0

4x² - 4x - 3 x + 3 = 0

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

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

x = 1 Or x = 3/4

number can be 1 or can be 3/4

$\huge \boxed{hope \: it \: helps...}$

@amansaini76⚠️

Answer 2

Answer: '1' or '3/4'

Let the number be x.

Four times the number = 4x

Three times the reciprocal = 3/x

$4x+\frac{3}{x}=7 \\ \\ 4x^2+3=7x \\ \\ 4x^2-7x+3=0$

$a=4\\ \\ b=-7 \\ \\ c=3 \\ \\ \\ b^2-4ac=(-7)^2-(4\times4\times3) \\ \\ b^2-4ac=49-48 \\ \\ b^2-4ac=1$

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ x=\frac{7\pm\sqrt{1}}{2\times4} \\ \\ x=\frac{7\pm1}{8} \\ \\ x=\frac{8}{8} \ \ \ \ \ \ \ \ \ \ OR \ \ \ \ \ \ \ \ \ \ x=\frac{6}{8} \\ \\ x=\bold{1} \ \ \ \ \ \ \ \ \ \ OR \ \ \ \ \ \ \ \ \ \ x=\bold{\frac{3}{4}}$

So the answer is '1' or '3/4'.

Thank you. ^_^