Question

Please find it a+1/a theory question (a+1/a)²=a²+1/a²​

Answer 1

Answer:

(i)2, (ii)2

Step-by-step explanation:

Just squaring both sides thrice and using basic formulas of algebra we can obtain the required answers.

Answer 2

Step-by-step explanation:

Given :-

a + (1/a) = 2

To find :-

Find the following :

(i) (a^4+1)/a^2

(ii) (a^8+1)/a^4

Solution :-

Given that :

a + (1/a) = 2 -------------(1)

On squaring both sides then

[a + (1/a)]^2 = 2^2

a^2 + 2(a)(1/a) + (1/a)^2 = 4

Since (a+b)^2 = a^2+2ab+b^2

=> a^2 + 2 + (1/a^2) = 4

=> a^2+(1/a^2) = 4 - 2

=> a^2 + (1/a^2) = 2 -----------(2)

=> [(a^2×a^2)+1]/a^2 = 2

=> (a^4 + 1)/a^2 = 2

Since (a^m)^n = a^mn

Again , On squaring both sides then

=> [a^2 + (1/a^2)]^2 = 2^2

=> (a^2)^2 + 2(a^2)(1/a^2) +(1/a^2)^2 = 4

Since (a+b)^2 = a^2+2ab+b^2

=> a^4 + 2 + (1/a^4) = 4

Since (a^m)^n = a^mn

=> a^4 + (1/a^4) = 4 - 2

=> a^4 + (1/a^4) = 2 ---------------(3)

=> [(a^4×a^4)+1]/a^4 = 2

=> (a^8+1)/a^4 = 2

Since (a^m)^n = a^mn

Answer :-

i) The value of (a^4+1)/a^2 is 2

ii) The value of (a^8+1)/a^4 is 2

Used formulae:-

• (a+b)^2 = a^2 + 2ab + b^2

• (a^m)^n = a^mn