Solve :-x2/3 +2x 1/3 - 3=0
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Answer:
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Your question is
2
3
+
2
1
3
−
3
=
0
\frac{x^{2}}{3}+\frac{2x^{1}}{3}-3=0
3x2+32x1−3=0
Quadratic formula
1
Multiply all terms by the same value to eliminate fraction denominators
2
3
+
2
1
3
−
3
=
0
\frac{x^{2}}{3}+\frac{2x^{1}}{3}-3=0
3x2+32x1−3=0
3
(
2
3
+
2
1
3
−
3
)
=
3
⋅
0
3(\frac{x^{2}}{3}+\frac{2x^{1}}{3}-3)=3 \cdot 0
3(3x2+32x1−3)=3⋅0
2
Simplify
Distribute
Cancel multiplied terms that are in the denominator
Cancel multiplied terms that are in the denominator
Multiply by zero
2
+
2
1
−
9
=
0
x^{2}+2x^{1}-9=0
x2+2x1−9=0
3
Rearrange terms
2
+
2
1
−
9
=
0
x^{2}+2x^{1}-9=0
x2+2x1−9=0
2
+
2
−
9
=
0
x^{2}+2x-9=0
x2+2x−9=0
4
Use the quadratic formula
=
−
±
2
−
4
√
2
x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}
x=2a−b±b2−4ac
Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.
2
+
2
−
9
=
0
x^{2}+2x-9=0
x2+2x−9=0
=
1
a={\color{#c92786}{1}}
a=1
=
2
b={\color{#e8710a}{2}}
b=2
=
−
9
c={\color{#129eaf}{-9}}
c=−9
=
−
2
±
2
2
−
4
⋅
1
(
−
9
)
√
2
⋅
1
x=\frac{-{\color{#e8710a}{2}} \pm \sqrt{{\color{#e8710a}{2}}^{2}-4 \cdot {\color{#c92786}{1}}({\color{#129eaf}{-9}})}}{2 \cdot {\color{#c92786}{1}}}
x=2⋅1−2±22−4⋅1(−9)
5
Simplify
Evaluate the exponent
Multiply the numbers
Add the numbers
Factorisation
Factorisation
Factorisation
Evaluate the square root
Evaluate the square root
Multiply the numbers
Multiply the numbers
=
−
2
±
2
1
0
√
2
x=\frac{-2 \pm 2\sqrt{10}}{2}
x=2−2±210
6
Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
=
−
2
+
2
1
0
√
2
x=\frac{-2+2\sqrt{10}}{2}
x=2−2+210
=
−
2
−
2
1
0
√
2
x=\frac{-2-2\sqrt{10}}{2}
x=2−2−210
7
Solve
Rearrange and isolate the variable to find each solution
=
−
1
+
1
0
√
x=-1+\sqrt{10}
x=−1+10
=
−
1
−
1
0
√
x=-1-\sqrt{10}
x=−1−10
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Solution
=
−
1
±
1
0
Step-by-step explanation:
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