Algebra For SBI PO : Set – 14

(1-5) In each of these questions, two equations are given. You have to solve these equations and find out the values of x and y and Give answer.

1)

a) If x>y

b) If x ≥ y

c) If x<y

d) If x ≤ y

e) If x=y or relationship cannot be established

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C)

x < y

2)

a) If x>y

b) If x ≥ y

c) If x<y

d) If x ≤ y

e) If x=y or relationship cannot be established

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a)

3)

a) If x>y

b) If x ≥ y

c) If x<y

d) If x ≤ y

e) If x=y or relationship cannot be established

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c)

solve the equation to get x < y

4)

a) If x>y

b) If x ≥ y

c) If x<y

d) If x ≤ y

e) If x=y or relationship cannot be established

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c)

We have 22x– 3 × 2x+ 2+ 32 = 0

22x – 3 × 2x × 22 + 32 = 0

22x – 12 × 2x + 32 = 0

y2– 12y + 32 = 0, where y = 2x

y2– 8y – 4y + 32 = 0

y (y – 8) – 4 (y – 8) = 0

(y – 8) (y – 4) = 0

y = 8 or y = 4

Now, y = 8 ⇒ 2x = 8 ⇒ 2x = 23x = 3

And y = 4 ⇒ 2x = 4 ⇒ 2x = 22x = 2

Hence, x = (2, 3)

y=(4, 8)

so relation is If x<y

5)

a) If x>y

b) If x ≥ y

c) If x<y

d) If x ≤ y

e) If x=y or relationship cannot be established

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I. 8×2 + 15 = 26x

⇒  8 – 26x + 15 = 0

[Putting in the form as ax2 + bx + c = 0]

⇒    8×2 – 20x – 6x + 15 = 0

⇒    4x (2x – 5) – 3 (2x – 5) = 0

⇒     (2x – 5) (4x – 3) = 0

⇒ 2x – 5 = 0 or 4x – 3 = 0  [Zero product rule]

⇒ x =  5/2     or x = 3/4

Hence, the roots of the given equation are x = (5/2, ¾).

II. Given y (2y + 5) = 25 ⇒ 2y2 + 5y – 25 = 0

[Putting in the form as ay2 + by + c = 0]

⇒       2y2 + 10y – 5y – 25 = 0

⇒       2y (y + 5) – 5 (y + 5) = 0

⇒       (y + 5) (2y – 5) = 0

⇒       y + 5 = 0 or 2y – 5 = 0

⇒       y = – 5 or y = 5/2

Hence, the roots of the given equation are y = (–5, 5/2).

(6-10) In the following questions there are two equations. Solve the two equations and answer appropriately:

6)

I. 6x²+5x+1=0

II. 5y²+8y+3=0

a) x<y

b) x<=y

c) x>y

d) x>=y

e) x=y or relationship cannot be established

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c)

7)

I. x²+7x+12=0

II. 2y²+5y+3=0

a) x<y

b) x<=y

c) x>y

d) x>=y

e) x=y or relationship cannot be established

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a)

8)

I. x²+7x+12=0

II. 2y²+5y+3=0

a) x<y

b) x<=y

c) x>y

d) x>=y

e) x=y or relationship cannot be established

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a)

9)

I. x²-19x+84=0

II. y²-25y+156=0

a) x<y

b) x<=y

c) x>y

d) x>=y

e) x=y or relationship cannot be established

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b)

10)

I. x²-9x+20=0

II. 2y²-7y+5=0

a) x<y

b) x<=y

c) x>y

d) x>=y

e) x=y or relationship cannot be established

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c)