(ii) 5x2 -6x-2 0

1.	(ii) 5x2 -6x-2 0
Answer» 5x^2 -6x -2 = 0 x^2 -(6/5)x -(2/5) = 0 (x)^2 - [2.(3/5).x] + (3/5)^2 - (3/5)^2 -(2/5) = 0 [x-(3/5)]^2 = (2/5)+(9/25) [x-(3/5)]^2 = (19/25) x-(3/5) = √19/5 x = (3/5) ± √19/5 Roots of the equation are x = [3+(√19)]/5& x = [3-(√19)]/5 Given: 5x^2-6x-2=0 Now we follow the algorithm Step-1: x^2-6÷5x-2÷5=0 (dividing both sides by 5 ) Step-2: x^2-6÷5=2÷5 Step-3: x^2-6÷5+[3÷5]^2=2÷5+[3÷5]^2 (adding [3÷5]^2 to both sides ) Step-4: [x-3÷5]^2=2÷5+9÷25 Step-5: [x-3÷5]^2=19÷25 Step-6: x-3÷5=+-√19÷25 Step-7: x=3÷5+√19÷5 or x=3÷5-√19÷5 Therefore... x=3+√19÷5 or x=3-√19÷5

Answer»

5x^2 -6x -2 = 0

x^2 -(6/5)x -(2/5) = 0

(x)^2 - [2.(3/5).x] + (3/5)^2 - (3/5)^2 -(2/5) = 0

[x-(3/5)]^2 = (2/5)+(9/25)

[x-(3/5)]^2 = (19/25)

x-(3/5) = √19/5

x = (3/5) ± √19/5

Roots of the equation are

x = [3+(√19)]/5& x = [3-(√19)]/5

Given: 5x^2-6x-2=0

Now we follow the algorithm

Step-1: x^2-6÷5x-2÷5=0 (dividing both sides by 5 )

Step-2: x^2-6÷5=2÷5

Step-3: x^2-6÷5+[3÷5]^2=2÷5+[3÷5]^2 (adding [3÷5]^2 to both sides )

Step-4: [x-3÷5]^2=2÷5+9÷25

Step-5: [x-3÷5]^2=19÷25

Step-6: x-3÷5=+-√19÷25

Step-7: x=3÷5+√19÷5 or x=3÷5-√19÷5

Therefore... x=3+√19÷5 or x=3-√19÷5

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