2x²+5x+1=x^2+2x-1

x²+3x+2=0

x²+2x+x+2=0

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

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

x=-2,-1

2y²-8y+1=-1

2y²-8y+2=0

y²-4y+1=0

(+4±√(16-4×1×1))/(2×1)=2±√12=2±√3

Ans : b. Hence, y>x

x²/2+x-1/2=1

x^2+2x-1=2

x^2+2x-3=0

x+3x-x-3=0

x(x+3)-1(x+3)=0

(x+3)(x-1)=0

x=-3, 1

3y²-10y+8=y^2+2y-10

2y^2-12y+18=0

y^2-6y+9=0

(y-3)^2=0

y=3, 3

Ans: b. y>x

4x²-20x+19=4x-1

4x^2-24x+20=0

x^2-6x+5=0

x^2-5x-x+5=0

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

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

x=5, 1

2y²=26y-84

y^2=13y-42

y^2-13y+42=0

y^2-7y-6y+42=0

y(y-7)-6(y-7)=0

(y-7)(y-6)=0

y=7,6

Ans: b. y>x

y²+y-1=4-2y-y²

2y²+3y-5=0

2y^2+5y-2y-5=0

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

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

y=-5/2, 1

x²/2-3/2 x=x-3

x^2-3x=2x-6

x^2-5x+6=0

x^2-3x-2x+2×3=0

x(x-3)-2(x-3)=0

(x-3)(x-2)=0

x=3, 2

Sol: a. x>y

6x²+13x=12-x

3x^2+7x-6=0

(x+3)(3x-2)=0

x= -3, 2/3

1+2y²=2y+5y/6

1+2y^2=17y/6 y

12y^2-17y+6=0

12y^2-8y-9y+6=0

4y(3y-2)-3(3y-2)=0

(3y-2)(4y-3)=0

y=2/3,3/4

Ans: e. x≤y

x²=169x=√169

x=±13

y-√144=0

y=√144

y=12

Ans: e. No relationship cannot be determined

12x²+11x+12=10x²+22x

2x^2-11x+12=0

2x^2-8x-3x+12=0

(x-4)(2x-3)=0

x=4,3/2

13y²-18y+3=9y²-10y

4y^2-8y+3=0

4y^2-6y-2y+3=0

(2y-3)(2y-1)=0

y=3/2,1/2

Ans: b. x≥y

18/x² +6/x-12/x² =8/x²

(18+16x-12)/x^2 =8/x^2

6x+6=8

x=2/6=0.33

y³+9.68+5.64=16.95

y^3=16.95-15.32

y^3=1.63

y=∛1.63

y=1.176

Ans: c. x < y

√1225x+√4900=0

35x+70=0

x=-70/35=-2

81^1/4  y+343^1/3 =0

3y+7=0

3y=-7

y=-7/3=-2.33

Ans: a. x>y

(2⁵+11³)/6=x³

(32+1331)/6=x³

1363/6=x^3

x³=227.167

4y³=-(589÷4)+5y³

4y³= -589/4+5y³

589/4=y³

y³=147.25

y=5.280

Ans: a. x>y