Q.1) If ^a/_b = ^c/_d = ²/₅ , then evaluate : - [a⁴ + c⁴ / b⁴ + d⁴]^1/₄

Let ^a/_b = ^c/_d = ²/₅ = k ....................(1)

^a/_b = ^c/_d = k

a = bk , c = dk

According to the question put the power of 4

a⁴ = k⁴b⁴....................(2)

c⁴ = k⁴d⁴....................(3)

Add equation (2) and (3)

a⁴ + c⁴ = k⁴b⁴ + k⁴d⁴

a⁴ + c⁴ = k⁴(b⁴ + d⁴)

a⁴ + c⁴ / b⁴ + d⁴ = k⁴....................(4)

putting the value from equation (4)

[a⁴ + c⁴ / b⁴ + d⁴]^1/₄ = [k⁴]^1/₄

Now from equation (1)

²/₅ = k

k = ²/₅