Question

6ав+3(а-в)²при а=√2и в=√3

Answer 1

$6ab + 3(a - b)^{2} = 6ab + 3a^{2} - 6ab + 3b^{2} = 3( a^{2} + b^{2} )$
При  $a = \sqrt{2}; b = \sqrt{3}$:
$3(2 + 3) = 15$.
Ответ: 15.

Answer 2

To evaluate the expression 6ав+3(а-в)² with a=√2 and b=√3, we substitute these values into the expression:

6(√2)(√3) + 3(√2 - √3)²

We simplify the expression within the parentheses first by expanding the square:

6(√2)(√3) + 3(2 - 2√2√3 + 3)

Simplifying further by multiplying and adding terms, we get:

6(√2)(√3) + 3(5 - 2√6)

We can simplify the first term by multiplying and getting:

6(√2)(√3) = 6(√6)

So, the final result is:

6(√6) + 3(5 - 2√6) = 15 - √54