Question

вычислить (3^0,5-5^0,5)^2:((2-15^0,25)(2+15^0,25))

Answer 1

(3^0,5-5^0,5)²:((2-15^0,25)(2+15^0,25))=

=((3^0,5)²-2*((3*5)^0,5)+(5^0,5)²):(2²-(15^0,25)²)=(3-2√15+5):(4-√15)=

=(8-2√15):(4-√15)=2*(4-√15)/(4-√15)=2.

Answer 2

$(3^{0,5}-5^{0,5})^2:(2-15^{0,25})(2+15^{0,25})=\\=(sqrt3-sqrt5)^2:(2-sqrt[4]{15})(2+sqrt[4]{15})=frac{3-2sqrt{15}+5}{4-sqrt[4]{15^2}}=frac{8-2sqrt{15}}{4-sqrt{15}}=\\=frac{2cdot (4-sqrt{15})}{4-sqrt{15}}=2$