## .When we divide the sum of −13 5 and 12 7 by the product of −31 7 and −1 2 ,we get

Question

.When we divide the sum of −13
5
and 12
7
by the product of −31
7
and −1
2
,we get
(a) -2/5 (b) 4/7 (c) 13/2 (d) -12/7

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1 week 2021-09-13T14:25:50+00:00 1 Answer 0 views 0

## Answers ( )

1. Step-by-step explanation:

(i) 2×2–7x+ 3 = 0

On dividing both sides of the equation by 2, we get

x2– 7x/2 +3/2=0

x2– 2 ×x× 7/4 +3/2=0

adding (7/4)2 and subtracting on LHS, we get

(x)2- 2 ×x× 7/4 + (7/4)2- (7/4)2+ 3/2=0

(x- 7/4)2= 49/16 – 3/2

(x- 7/4)2= 25/16

(x- 7/4) =± 5/4

x= 7/4± 5/4

x= 7/4+ 5/4 orx= 7/4 – 5/4

x= 12/4 orx= 2/4

x= 3 or 1/2

(ii) 2×2+x– 4 = 0

On dividing both sides of the equation, we get

x2+x/2 – 2=0

adding (1/4)2and Subtracting to LHS, we get

(x)2+2 ×x× 1/4 + (1/4)2- (1/4)2 -2 =0

(x+ 1/4)2= 33/16

⇒x+ 1/4 = ± √33/4

⇒x= ± √33/4 – 1/4

⇒x= ± √33-1/4

⇒x= √33-1/4 orx= -√33-1/4

(iii) 4×2+ 4√3x+ 3 = 0

(2x)2+ 2 × 2x× √3+ (√3)2= 0

(2x+ √3)2= 0

(2x+ √3) = 0 and (2x+ √3) = 0

x= -√3/2 orx= -√3/2

(iv) 2×2+x+ 4 = 0

On dividing both sides of the equation, we get

x2+ 1/2x+2=0

Adding and Subtracting (1/4)2to LHS, we get

(x)2+2 ×x× 1/4 + (1/4)2- (1/4)2+ 2=0

(x+ 1/4)2= 1/16 – 2

(x+ 1/4)2= -31/16

However, the square of number cannot be negative.

Therefore, there is no real root for the given equation