Wiedzac, że... oblicz wartość wyrażenia

[Sallatta]

Sinxcosx=\(\frac{ \sqrt{5} }{4}\), oblicz
A) \(sin^4 x+cos^4 x\)
B) \(sin^6 x +cos^6 x\)

[heja]

A)\(\sin ^{2}x \cos ^{2}x= \frac{5}{16}\)
\(\sin ^{4}x+ \cos ^{4}x=( \ sin^{2}x)^{2}+( \cos ^{2}x)^{2}+2 \sin ^{2}x \cos ^{2}x-2 \sin ^{2}x \cos ^{2}x=( \sin ^{2}x+ \cos ^{2}x)^{2}-2 \sin ^{2}x \cos ^{2}x=\)
\(=1-2 \cdot ( \frac{ \sqrt{5} }{4})^{2}= \frac{3}{8}\)

[heja]

B)\(\sin ^{6}x+ \cos ^{6}x=( \sin ^{2}x)^{3}+( \cos ^{2}x)^{3}=( \sin ^{2}x+ \cos ^{2}x)( \sin ^{4}x+ \cos ^{4}x- \sin ^{2}x \cos ^{2}x)= \frac{1}{16}\)