Q. prove that the equation ,`(sin^-1)^3+(cos^-1)^3=alpha pi^3` has no root for `alpha<1/32`

IF one root of the quadratic equation x^2-x-1=0 is alpha , prove that its other root is alpha^3-3alpha .

Q. Prove that from the equality sin^4 alpha/a+cos^4 alpha/b=1/(a+b) follows the relation; sin^8 alpha/a^3+cos^8 alpha/b^3=1/(a+b)^3.

Prove that from the equality (sin^(4)alpha)/a+(cos^(4)alpha)/b=1/(a+b) follows the relations, (sin^(8)alpha)/a^(3) +(cos^(8)alpha)/b^(3)=1/(a+b)^(3)

Q.Prove that from the equality (sin^(4)alpha)/(a)+(cos^(4)alpha)/(b)=(1)/(a+b) follows the relation; (sin^(8)alpha)/(a^(3))+(cos^(8)alpha)/(b^(3))=(1)/((a+b)^(3))

If 1 lies between the roots of the equation 3x^(2)-(3sin alpha)x-2cos alpha=0 then alpha lies in the interval:

Prove that from the equality (sin^(4)alpha)/(a)+(cos^(4)alpha)/(b)=(1)/(a+b) follow the relation :(sin^(8)alpha)/(a^(3))+(cos^(8)alpha)/(b^(3))=(1)/((a+b)^(3))

If alpha is a root of the equation 4x^2+2x-1=0, then prove that 4alpha^3-3alpha is the other root.

If alpha is a root of the equation 4x^2+2x-1=0, then prove that 4alpha^3-3alpha is the other root.

If alpha is a root of the equation 4x^2+2x-1=0, then prove that 4alpha^3-3alpha is the other root.