Question

найдите значение выражения 5ab/a+5b * (a/5b-5b/a)
при a=5√2+4 b=√2-3

Answer 1

5ab/(a+5b)×(a/5b-5b/a)
при a=5√2+4 b=√2-3

5ab/(a+5b)×(a/5b-5b/a)=1

1) (a/5b)-(5b/a)=(a²-(5b)²)/5ba
2) (5ab/(a+5b))×(a-5b)(a+5b)/5ab=(5ab×(a-5b)×(a+5b))/(5ab×(a+5b))=(a-5b)

(a-5b)=5√2+4-5×(√2-3)=5√2+4-5√2-3=4-3=1