How much photoperiod (hours) is required by long day

If a + b² + c² = 16, x² + y² + z² = 25 and ax + by + cz = 20, then the value of (a+b+c)/(x+y+z)

If a³ + 3a² + 9a = 1, then what is the value of a³ + (3/a)?

Find x, given 5 (√5)^x+6 = (√5)^2x+7 :

The value of the expression (1 + sec22° + cot68°)(1 – cosec22° + tan68°) is

Which is the largest six digit number, which when divided by 12, 15, 20, 24 and 30, leaves the remainders 8, 11, 16, 20 and 26 respectively.

If 2cos² Ɵ – 5cos Ɵ + 2 = 0,0⁰ < Ɵ < 90⁰ , then the value of (cosec Ɵ + cot Ɵ) is :

Solve for x (x > 1):

log₃(x − 1) + log₃(x + 1) = 2

If x1x2x3 = 4(4 + x1 + x2 + x3), then what is the value of [1/(2 + x1)] + [1/(2 + x2)] + [1/(2 + x3)]?

If (x - 1/x)² = 3, then the value of x⁶ + 1/x⁶ equals

If α and β are the roots of equation x² – x + 1 = 0, then which equation will have roots α³ and β³?