Question

4x+4/x =17 find quadratic equations.

Answer 1

Answer:

Step-by-step explanation:4x^2-17x+4

Will be the answer .

Answer 2

$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: SOLUTION\: \: \red{ \mid}}}}}}}}$




$\underline{\underline{\bold{ \: (1) \: \: Calculation \: \: for \: \: finding \: \: the \: \:}}}\\ \underline{\underline{\bold{ \: \: Quadratic \: \:equation \: \: : }}}$


$\bold{ \: \: \: \: \: \: \: \: \: 4x + \frac{4}{x} = 17} \\ \\ \bold{\Longrightarrow \:{ \frac{ 4x {}^{2} + 4}{x} = 17} }\\ \\ \bold{ \Longrightarrow \: 4x {}^{2} + 4 =17x } \\ \\ \bold{ \therefore \: \: 4x {}^{2} - 17x + 4 = 0}$



$\bold{ \therefore \: \: The \: \: quadratic \: \: equation \: \: is \: : } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \boxed{ \bold{ \red{ \: \: 4x {}^{2} - 17x + 4 = 0 \: \: }}}}$



$\underline{ \underline{ \bold{ \: (2) \: \: Calculation \: \: for \: \: finding \: \: the \: roots \: \: : \: \: }}}$



$\bold{ \: \: \: \: \: \: \: 4x {}^{2} - 17x + 4 = 0} \\ \\ \bold{ \Longrightarrow \: 4x {}^{2} - 16x - x + 4 = 0} \\ \\ \bold{ \Longrightarrow \: 4x(x - 4) - 1(x - 4) = 0} \\ \\ \bold{ \Longrightarrow \: (x - 4)(4x - 1) = 0}$



$\bold{ \therefore \: \: \: x - 4 = 0} \\ \\ \bold{ \Longrightarrow \: x = 4} \\ \\ \\ \bold{OR,} \\ \\ \\ \bold{4x - 1 = 0 }\\ \\ \bold{ \Longrightarrow \: 4x = 1} \\ \\ \bold{ \Longrightarrow \: x = \frac{1}{4} }$



$\bold{ \therefore \: \: The \: \: roots \: \: of \: \: the \: \: quadratic \: \: } \\ \\ \bold{equation \: \: \: is \: \: : \: \: \red{x = 1 \: \: \: Or, \: \: \: x = \frac{1}{4} }}$