Answer:
see explanation
see explanationStep-by-step explanation:
21
Note that
(a - [tex]\frac{1}{a}[/tex])²
= a² - 2 + [tex]\frac{1}{a^2}[/tex]
= a² + [tex]\frac{1}{a^2}[/tex] - 2
= 11 - 2
= 9
Thus
(a - [tex]\frac{1}{a}[/tex])² = 9 ( take the square root of both sides )
a - [tex]\frac{1}{a}[/tex] = 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
