Question

Can anyone answer these questions

Answer 1

see explanation

see explanationStep-by-step explanation:

21

Note that

(a -
`(1)/(a)`)²

= a² - 2 +
`(1)/(a^2)`

= a² +
`(1)/(a^2)` - 2

= 11 - 2

= 9

Thus

(a -
`(1)/(a)`)² = 9 ( take the square root of both sides )

a -
`(1)/(a)` = 3

22

Since the expression is a perfect square, then

(4x + 5y)²

= 16x² + 40xy + 25y²

Comparing coefficients, then

a - 1 = 40 ( add 1 to both sides )

a = 41

23

99² - 87² ← is a difference of squares and factors as

= (99 - 87)(99 + 87)

= 12 × 186 = 1152, thus

24a = 1152 ( divide both sides by 24 )

a = 48