Question

If √a²+b²=197 then a+b is ?

Answer 1

Answer:

√a²+b²=197

=We see if (a,b,197) is a Pythagorean triple

let b = 197-k

=>a² + (197-k)²=197²

=> a² + 197² -1226k + k²=197²

=> a² - 1226k + k² = 0

we know that √1226=35.011

So the largest square not exceeding 1226 is 35² = 1225

So we write 1226 = 35² + 1 a² - (35²+1)k + k² = 0

a² = (35²+1)k - k²

a² = 35²k + k - k²

We see that if k=1 the right side becomes 35

Therefore k=1, and b = 197-k = 197-1 = 196and a=35²

Therefore (a,b,197) = (35,196,197) is a Pythagorean triple.

Thus a+b = 35+197=232

Explanation:

hope it helps