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Solve:
x + 1/x = 4 1/4


Ans: 4,1/4​

Solve: x + 1/x = 4 1/4 Ans: 4,1/4​-example-1

2 Answers

6 votes

Answer:


\boxed{x = (1)/(4)} and
\boxed{x = 4}

Explanation:

Given equation:


x + (1)/(x) = 4(1)/(4)

Step-1: Convert the mixed fraction on the R.H.S into improper fraction


x + (1)/(x) = 4(1)/(4)


x + (1)/(x) = (4 *4 + 1)/(4)


x + (1)/(x) = (16 + 1)/(4)


x + (1)/(x) = (17)/(4)

Step-2: Make common denominators on the L.H.S:


x + (1)/(x) = (17)/(4)


(x^(2) )/(x) + (1)/(x) = (17)/(4)

Step-3: Combine the denominators on the L.H.S


(x^(2) )/(x) + (1)/(x) = (17)/(4)


(x^(2) +1)/(x) = (17)/(4)

Step-4: Use cross multiplication


(x^(2) +1)/(x) = (17)/(4)


x^(2) +1} = (17x)/(4)


4(x^(2) +1}) = {17x}

Step-5: Simplify the distributive property


4(x^(2) +1}) = {17x}


4x^(2) +4} = {17x}


-17x + 4x^(2) +4} = 0

Step-6: Change "-17x" to "-16x - x" as it is equivalent


-17x + 4x^(2) +4} = 0


(-16x - x) + 4x^(2) +4} = 0

Step-7: Factor the common terms


(-16x - x) + 4x^(2) +4} = 0


-16x - x + 4x^(2) +4} = 0


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

Step-8: Group the terms


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


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

Step-9i: Use cross multiplication for (x - 4)


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


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

Step-9ii: Use cross multiplication for (4x - 1)


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


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

Thus
x - 4 = 0 and
4x - 1 = 0.

Step-10: Simplify both equations


4x - 1 = 0
x - 4 = 0


4x = 0 + 1
x = 0 + 4


4x = 1
\boxed{x = 4}


\boxed{x = (1)/(4)}

User Chris Fulstow
by
8.1k points
8 votes

Answer:

x = 4, 1/4

solving steps


\sf \rightarrow x + (1)/(x)=4(1)/(4)

make the denominators same


\sf \rightarrow (x(x))/(x) + (1)/(x)=4(1)/(4)

simplify the following


\sf \rightarrow (x^2)/(x) + (1)/(x)=(17)/(4)

join both fractions together


\sf \rightarrow (x^2+1)/(x)=(17)/(4)

cross multiply


\sf \rightarrow 4(x^2+1)=17(x)

simplify


\sf \rightarrow 4x^2-17(x)+4=0

completing square


\sf \rightarrow 4x^2-16(x)-x+4=0

factor


\sf \rightarrow 4x(x-4)-1(x-4)=0

group the variables


\sf \rightarrow (4x-1)(x-4)=0

simplify


\sf \rightarrow (x-4)=0, \ (4x-1) =0

final answer


\sf \rightarrow x=4, \ x =(1)/(4)

User Christian Fosli
by
8.3k points

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