# Quadratic equation/Algebra Questions – Set 34

Directions (Q. Nos. 1 to 5) In the following questions, two equations A and B are given. You have to solve both the equations and

1. If x>y
2. If x<y
3. If x=y
4. If xy
5. If xy

1) 2x2+5x+1=x^2+2x-1

2y2-8y+1=-1

Sol:

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

2) x2/2+x-1/2=1

3y2-10y+8=y^2+2y-10

Sol:

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

3) 4x2-20x+19=4x-1

2y2=26y-84

Sol:

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

4) y2+y-1=4-2y-y2

x2/2-3/2 x=x-3

Sol:

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

5) 6x2+13x=12-x

1+2y2=2y+5y/6

Sol:

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

Directions (Q. Nos. 6 to 10) In the following questions, two equations A and B are given. You have to solve both the equations and

1. If x>y
2. If x≥y
3. If x<y
4. If x≤y
5. If x=y or the relationship cannot be established

6) x2=169

y-√144=0

Sol:

x2=169x=√169

x=±13

y-√144=0

y=√144

y=12

Ans: e. No relationship cannot be determined

7) 12x2+11x+12=10x2+22x

13y2-18y+3=9y2-10y

Sol:

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

8) 18/x2 +6/x-12/x2 =8/x2

y3+9.68+5.64=16.95

Sol:

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

9) √1225x+√4900=0

811/4  y+3431/3 =0

Sol:

√1225x+√4900=0

35x+70=0

x=-70/35=-2

811/4  y+3431/3 =0

3y+7=0

3y=-7

y=-7/3=-2.33

Ans: a. x>y

10) (25+113)/6=x3

4y3=-(589÷4)+5y3

Sol:

(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