Question

if x+1/x =17/4 then find x​

Answer 1

Solution :-

⇒ x + 1/x = 17/4

Taking LCM

⇒ (x² + 1)/x = 17/4

By Cross multiplication

⇒ 4(x² + 1) = 17x

⇒ 4x² + 4 = 17x

⇒ 4x² - 17x + 4 = 0

Splitting the middle term

⇒ 4x² - 16x - x + 4 = 0

⇒ 4x(x - 4) - 1(x - 4) = 0

⇒ (4x - 1)(x - 4) = 0

⇒ 4x - 1 = 0 or x - 4 = 0

⇒ 4x = 1 or x = 4

⇒ x = 1/4 or x = 4

Therefore the value of x is 1/4 or 4.

Answer 2

$\huge\mathbb{\underline{SOLUTION:-}}$

$\sf\underline{\purple{Given:-}}$

$\sf\bullet x+\dfrac{1}{x}=\dfrac{17}{4}$

$\sf\underline{\purple{Solution:-}}$

$\sf\implies x+\dfrac{1}{x}=\dfrac{17}{4}\\ \\ \sf\:\:By\: taking\:L.C.M\\ \\ \sf\implies \dfrac{x{}^{2}+1}{x}=\dfrac{17}{4}\\ \\ \sf\:\:\:Cross\: multiplication\\ \\ \sf\implies 4(x{}^{2}+1)=17\times x\\ \\ \sf\implies 4x{}^{2}+4=17x\\ \\ \sf\implies 4x{}^{2}-17x+4=0\\ \\ \sf\:\:\:\: Factor\:of\:16=16\times 1\\ \\ \sf\implies 4x{}^{2}-(16+1)x+4=0\\ \\ \sf\implies 4x{}^{2}-16x-x+4=0\\ \\ \sf\implies 4x(x-4)-1(x-4)=0\\ \\ \sf\implies {\red{(x-4)(4x-1)}}=0\\ \\ \sf\:\:\:i) \:\:x-4=0\\ \sf\implies x=4\\ \\ \sf\:\:\:\:ii)\:\:4x-1=0\\ \sf\implies 4x=1\\ \\ \sf\implies x=\dfrac{1}{4}$

The value of x is

$\boxed{\sf{x=4\:\:or\:\dfrac{1}{4}}}$