Question

solve the following quadratic equation by using quadratic formula factorization and completing the square method:

Q. 10x - 1/x =3​

Answer 1

Answer:

10x-1/x=3

10x²-3x-1=0

10x²-5x+2x-1=0

5x(2x-1)+1(2x-1)=0

(5x+1)(2x-1)=0

x=-1/5 or x=1/2

Answer 2

Answer:

True

Step-by-step explanation:

Given equation is 10x− x1 =3

Multiplying both sides by x,⇒ 10x 2 −1=3x

Now, dividing both sides by 10 we get,⇒ x 2 − 101=103x⇒ x 2 − 103 x− 101 =0Here, a=1,b=− 103 ,c=−101⇒ x 2 − 103 x= 101 Now, ( 2b ) 2 =(− 2×103 )2= 4009 Adding 4009 on both sides,⇒ x 2 − 103 x+ 4009 = 101 + 4009 Using the algebraic property (a−b) 2 =a 2 −2ab+b 2 , we can write the above equation as:(x− 203 ) 2 = 40049 Taking square root on both sides,x− 203 =±

207⇒ x= 207+3 or x= 20−7+3⇒ x= 21 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.