Question

The sum of a number and its reciprocal is 17/4. Find the number.​

Answer 1

Answer:

X=4or1/4

Step-by-step explanation:

Let the number be x. Then,

X+1/X=17/4

4X²+4=17X

4X²-17X+4=0

4X²-16X-X+4=0

4X(X-4)-1(X-4)=0

(X-4)(4X-1)=0

Either, X=4

or, X=1/4

Answer 2

✍️${\huge{\purple{\underline{\underline{Question}}}}}$✍️

The sum of a number and its reciprocal is 17/4. Find the number.

✍️${\huge{\purple{\underline{\underline{Answer}}}}}$✍️

✈️${\red{\underline{Given}}}$✈️

Let the no. be x

$x+\frac{1}{x}=\frac{17}{4}$

✈️${\red{\underline{To\ find}}}$✈️

Number=Value of x=????

✈️${\red{\underline{Solution}}}$✈️

$x+\frac{1}{x}=\frac{17}{4}$

Multiply all the terms by 4x.

$(4x×x)+(4x×\frac{1}{x})=(4x\frac{17}{4})$

$=>{4x}^{2}+4×\frac{\cancel4x}{\cancel4}=\frac{\cancel4 x×17}{\cancel4}$

$=>{4x}^{2}+4=17x$

$=>{4x}^{2}+4-17x=0$

$=>{4x}^{2}-17x+4=0$

$=>{4x}^{2}-16x-x+4=0$

$=>4x(x-4)-1(x-4)=0$

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

So,

Either;

$4x-1=0\\</p><p>=>4x=0+1\\</p><p>=>x=\frac{1}{4}$

Or

$x-4=0\\</p><p>=>x=0+4\\</p><p>=>x=4$

$Hence,\ solution\ is\ number\ is\ 4\ or\ \frac{1}{4}$