Question

If a+1/a=5 find the difference between a and 1/a .

Answer 1

Answer:

sqrt21

Step-by-step explanation:

a+1/a =5

square on both sides

(a+1/a)^2 = 5^2 ((a+b)^2=a^2+b^2+2ab)

a^2 +1/a^2 +2×a×1/a =25

a^2+1/a^2+2 =25

deduct 4 on both sides of equation

a^2+ 1/a^2-2=21

a^2+1/a^2-2×(a×1/a)= 21 (a×1/a=1, so 2= 2×a×1/a)

it is in form a^2-2ab+b^2=(a-b)^2

(a- 1/a)^2=21

(a-1/a)=sqrt(21)

hope this helps

Answer 2

Answer:

$(a-\frac{1}{a} )=\sqrt{21}$

Step-by-step explanation:

$a+\frac{1}{a} = 5$

Squaring both the sides,

$(a+\frac{1}{a} )^2 = 25$

⇒ $a^{2} +\frac{1}{a^{2} } +2 = 25$

⇒$a^{2} +\frac{1}{a^{2} } = 23$

Now,

$(a - \frac{1}{a} )^2=a^{2} +\frac{1}{a^{2} } -2$

∵ $a^{2} +\frac{1}{a^{2} } = 23$

∴ $(a-\frac{1}{a} )^2= 23-2$

⇒ $a-\frac{1}{a} = \sqrt{21}$