Question

在三角形abc中BC=a,AC=b,AB=c,且满足a^4+b^4+0.5c^4=a^2c^2+b^2c^2,求三角形A

Answer 1

a^4+b^4+0.5c^4=a^2c^2+b^2c^2

a^4+b^4+0.5c^4-a^2c^2-b^2c^2=0

a^4-a^2c^2+0.25c^4+b^4-b^2c^2+0.25c^4=0

(a^2-0.5c^2)^2+(b^2-0.5c^2)^2=0

a^2=0.5c^2

b^2=0.5c^2

a^2+b^2=c^2

a=b

等腰直角三角形