Question

If a=3+2 underroot 2 then the value of a power1/2 - a power -1/2

Answer 1

Answer:

here u go................

Step-by-step explanation:

The last digit of 3 in positive integer power repeats in pattern of 4: {3, 9, 7, 1}. So, basically we should find the remainder upon division 7^(11) by cyclicity of 4 (to see on which number in this pattern falls on). , now if we expand this expression all terms but the last one will have 4 in them, thus will leave no remainder upon division by 4, the last term will be . Thus the question becomes: what is the remainder upon division by 4:

3 divided by 4 yields remainder of 3;

3^2=9 divided by 4 yields remainder of 1;

3^3=27 divided by 4 yields remainder of 3;

3^4=81 divided by 4 yields remainder of 1.

So, 3 in odd power yields remainder of 3 upon division by 4 --> yields remainder of 3 --> finally, we have that will have the same last digit as , which is 7. Thus as has the last digit of 7 then divided by 5 it will yield remainder of 2.