plz answer this question fast
Answers
Step-by-step explanation:
The roots are x=\frac{3+\sqrt{5}}{2},\frac{3-\sqrt{5}}{2}x=
2
3+
5
,
2
3−
5
Step-by-step explanation:
Given : Expression x+\frac{1}{x}=3;x\neq 0x+
x
1
=3;x
=0
To find : The roots of the given expression?
Solution :
We write the given expression in simpler form,
x+\frac{1}{x}=3x+
x
1
=3
\frac{x^2+1}{x}=3
x
x
2
+1
=3
x^2+1=3xx
2
+1=3x
x^2-3x+1=0x
2
−3x+1=0 is the quadratic equation.
Using quadratic formula,
General form - ax^2+bx+c=0ax
2
+bx+c=0 D=b^2-4acD=b
2
−4ac
Solution is x=\frac{-b\pm\sqrt{D}}{2a}x=
2a
−b±
D
Equation is x^2-3x+1=0x
2
−3x+1=0
where, a=1 , b=-3, c=1
D=b^2-4acD=b
2
−4ac
D=(-3)^2-4(1)(1)D=(−3)
2
−4(1)(1)
D=9-4D=9−4
D=5D=5
Solution is x=\frac{-b\pm\sqrt{D}}{2a}x=
2a
−b±
D
x=\frac{-(-3)\pm\sqrt{5}}{2(1)}x=
2(1)
−(−3)±
5
x=\frac{3\pm\sqrt{5}}{2}x=
2
3±
5
Therefore, The roots are x=\frac{3+\sqrt{5}}{2},\frac{3-\sqrt{5}}{2}x=
2
3+
5
,
2
3−
5
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