Question

find this answer using identity

Answer 1

1. a - 1/a = 5
take square both side
a^2+1/a^2-2 =25
a^2 + 1/a^2 =27

2. b + 1/b =7
take square both side
b^2 + 1/b^2 + 2.b.1/b = 49
b^2 + 1/b^2 = 47

3. (i) (105)^2
use identity
( a + b)^2 = a^2 +b^2 + 2ab

(100 + 5)^2 =(100)^2 +(5)^2 +2. (100)(5)
=10000 + 25 +1000
=11025

same way another you can solve

for (ii) use identity
(a-b)^2 = a^2 + b^2 -2ab

(iii) use identity
a^2 - b^2 =(a-b)(a+b)

3. 25x^2 + 9y^2 + 30xy
=>(5x)^2 + (3y)^2 +2. (5x)(3y)
=>{5x+3y}^2

now you put value of x and y
{ 5 x 4 + 3 x 5}^2
=>(20+15)^2 =(35)^2 =1225