Question

Find the HCF of 65 and 117 and find a pair of integral values of m and n such that HCF = 65 ^m + 117^n ?​

Answer 1

Your answers is given below --->>>>

By Euclid's division algorithm

117 = 65x1 + 52.

65 = 52x1 + 13

52 = 13x4 + 0

Therefore 13 is the HCF (65, 117).

Now work backwards:

13 = 65 + 52x(-1)

13 = 65 + [117 + 65x(-1)]x(-1)

13 = 65x(2) + 117x(-1).

∴ m = 2 and n = -1.

Answer 2

Step-by-step explanation:

the principal amount be equal to P. Let the rate at which the interest is levied is equal to R% per annum (per year). let the time for which the amount is lent = T years. Then we can write:

Simple Interest = [{P×R×T}/100]

We can also calculate the Principal amount as P = [{100×(Simple Interest)}/(R×T)].

Similarly, we can write the time T as equal to T