Question

(5^-1 - 10^-1)^-1 + (3^-1 - 5^-1 - 5^-1) ^-1 find value (the answer is 17) how​

Answer 1

Solution :-

we know That, (a)^(-b) = 1/a^b and, (1/a)^-1 = a

→ (5^-1 - 10^-1)^-1 + (3^-1 - 5^-1 - 5^-1)^-1

Solving Part 1 :-

→ (5^-1 - 10^-1)^-1

→ [ 1/5 - 1/10 ]^-1

→ [ (2 - 1)/10]^-1

→ (1/10)^-1

→ 10 ------------- Equation (1).

_____________

Similarly, Solving Second Part :-

→ (3^-1 - 5^-1 - 5^-1)^-1

→ (1/3 - 1/5 - 1/5)^-1

→ (1/3)^-1

→ 3 ---------------- Equation (2).

_______________

Putting Both Values now we get,

→ (5^-1 - 10^-1)^-1 + (3^-1 - 5^-1 - 5^-1)^-1

→ 10 + 3

→ 13 (Ans).

Answer 2

Step-by-step explanation:

(5^-1 - 10^-1)^-1 + (3^-1 - 5^-1 - 5^-1) ^-1

= ( 1/5 - 1/10 )^-1 + ( 1/3 - 1/5 -1/5 )^-1

= ( (2 - 1)/10 )^-1 + ( 1/3 - 1/5 -1/5 )^-1

= (1/10)^-1 + (1/3 - 2/5)^-1

= 10 + ((5 - 2*3)/15)^-1

= 10 + (-1/15)^-1

= 10 + (-15)

= 10 - 15

= -5

Points:

• 2^-1 = 1/2, valid for any real number x
• (1/2)^-1 = 2, valid for any real number x

Thanks!