Question

1. if a+1/a= 17/4 then a-1/a=question mark (a) 13/4 (b)15/4 (c) 8/5 (d) 2/3
2. area of square is 4×2+12×+9 square units then length of each sides of the square is (a) (4×+3)u (b) (4×+9 (c) (x+3) (d) (2×3)​

Answer 1

Answer:

ANS 1: option:(b)

Explantion:

(a - 1/a)2 = (a + 1/a)2 - 4

= (17/4)2 - 4

= 289/16 - 4

= 225/16

= (15/4)2

a - 1/a = 15/4

Answer 2

Step-by-step explanation:

Solution :-

1)

Given that

a+(1/a) = 17/4

=> (a²+1)/a = 17/4

On applying cross multiplication then

=> 4(a²+1) = 17×a

=> 4a²+4 = 17a

=> 4a²+4-17a = 0

=> 4a²-17a+4 = 0

=> 4a²-16a-a+4 = 0

=> 4a(a-4)-1(a-4) = 0

=> (a-4)(4a-1) = 0

=> a-4 = 0 or 4a-1 = 0

=> a = 4 or 4a = 1

=> a = 4 or a = 1/4

Case -1:-

If a = 4 then 1/a = 1/4

now,

a-(1/a)

=> 4-(1/4)

=> (16-1)/4

=> 15/4

Case-2:-

If a = 1/4 then 1/a = 1/(1/4) = 4

Now,

a -(1/a)

=> (1/4)-4

=> (1-16)/4

=> -15/4

If we take positive value then a-(1/a) = 15/4

2)

Given that

Area of a square = 4x²+12x+9 sq.units

It can be written as

=> (2x)²+2(2x)(3)+(3)²

It is in the form of a²+2ab+b²

Where, a = 2x

and b = 3

We know that

(a+b)² = a²+2ab+b²

=> (2x)²+2(2x)(3)+(3)²

=> (2x+3)²

=> (2x+3)(2x+3)

We know that

Area of a square = Side × Side sq.units

=> Side × Side = (2x+3)(2x+3)

Side of the square = 2x+3 units

Used formulae:-

→ (a+b)² = a²+2ab+b²

→ Area of a square = Side × Side sq.units