Question

Solve the following for x: √2 x2 + 7x + 5√2 = 0​

Answer 1

Step-by-step explanation:

√2x²+7x+5√2=0

√2x²+2x+5x+5√2=0

√2x(x+√2)+5(x+√2)=0

(√2x+5) (x+√2)=0

√2x+5=0

√2x= -5

x = -5/√2

x+√2=0

x= -√2= -1.414

Answer 2

2x2 – x +1/8 = 0

Taking LHS,

=1/8 (16x2  – 8x + 1)

= 1/8 (16x2  – 4x -4x + 1)

= 1/8 (4x(4x  – 1) -1(4x – 1))

= 1/8 (4x – 1)2

The roots of this equation, 2x2 – x + 1/8 = 0, are the values of x for which (4x – 1)2= 0

Therefore, (4x – 1) = 0 or (4x – 1) = 0

⇒ x = 1/4 or x = 1/4