Question

Помогите доказать тождества!!!
(3a+b)^2+(a-3b)^2=10(a^2+b^2)

Answer 1

9a^2+6ab+b^2+a^2-6ab+9b^2= 10a^2+10b^2= 10(a^2+b^2) ч.т.д

Answer 2

Пусть а=х , b=y тогда,

$9 {x}^{2} + 6xy + {y}^{2} + {x}^{2} - 6xy + 9 {y}^{2} = 10 {x}^{2} + 10 {y}^{2} \\ 10 {x}^{2} + 10 {y}^{2} = 10 {x}^{2} + 10 {y}^{2} \\ 10( {x}^{2} + {y}^{2}) = 10( {x}^{2} + {y}^{2} ) \\ {x}^{2} + y^{2} = \frac{10( {x}^{2} + {y}^{2}) }{10} \\ {x}^{2} + {y}^{2} = {x}^{2} + {y}^{2}$