(vi) 10x =3, x = 0 ,+ – 1 x
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Class 10
>>Maths
>>Quadratic Equations
>>Solutions of Quadratic Equations
>>The equation 10x - 1x = 3 when solved by
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The equation 10x−
x
1
=3 when solved by the method of completing the square yields x = 0.5.
Medium
Solution
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Correct option is A)
Given equation is 10x−
x
1
=3
Multiplying both sides by x,
⇒ 10x
2
−1=3x
Now, dividing both sides by 10 we get,
⇒ x
2
−
10
1
=
10
3
x
⇒ x
2
−
10
3
x−
10
1
=0
Here, a=1,b=−
10
3
,c=−
10
1
⇒ x
2
−
10
3
x=
10
1
Now, (
2
b
)
2
=(−
2×10
3
)
2
=
400
9
Adding
400
9
on both sides,
⇒ x
2
−
10
3
x+
400
9
=
10
1
+
400
9
Using the algebraic property (a−b)
2
=a
2
−2ab+b
2
, we can write the above equation as:
(x−
20
3
)
2
=
400
49
Taking square root on both sides,
x−
20
3
=±
20
7
⇒ x=
20
7+3
or x=
20
−7+3
⇒ x=
2
1
or x=
5
−1
∴ x=0.5 and x=−0.2
Answer:
Given equation is 10x−
x
1
=3
Multiplying both sides by x,
⇒ 10x
2
−1=3x
Now, dividing both sides by 10 we get,
⇒ x
2
−
10
1
=
10
3
x
⇒ x
2
−
10
3
x−
10
1
=0
Here, a=1,b=−
10
3
,c=−
10
1
⇒ x
2
−
10
3
x=
10
1
Now, (
2
b
)
2
=(−
2×10
3
)
2
=
400
9
Adding
400
9
on both sides,
⇒ x
2
−
10
3
x+
400
9
=
10
1
+
400
9
Using the algebraic property (a−b)
2
=a
2
−2ab+b
2
, we can write the above equation as:
(x−
20
3
)
2
=
400
49
Taking square root on both sides,
x−
20
3
=±
20
7
⇒ x=
20
7+3
or x=
20
−7+3
⇒ x=
2
1
or x=
5
−1
∴ x=0.5 and x=−0.2
∴ Solving the given equation by completing the square method yields x=0.5.
Hence, the given statement is true.