Question

Factorize
(y) = y² +( 3 under root 5 /2 )y - 5 ​

Answer 1

y^2 + 3√5/2y -5

By Middle Term Splitting

y^2 + 4√5/2y - √5/2y - 5

Taking LCM

2y^2 + 4√5y -√5y -10 = 0

(Taking Denominator to RHS)

2y(Y +2√5) -√5(Y +2√5) =0

(Y + 2√5)(2y - √5) = 0

Two cases can be formed

If Y +2√5 = 0

Y = -2√5

If 2y - √5 = 0

Y = √5/2

Answer 2

Splitting the middle term

y²+4/2√5y-√5/2y-5=0

Taking LCM

2y²+4√5y-√5y-10=0 (Denominator taken to RHS)

2y(y+2√5)-√5(y+2√5)=0

(2y-√5)(y+2√5)=0

∴y= √5/2 or -2√5

Hope you understood :)