Question

-16ab+8(a+b)^2 при a=√2 b=√5

Answer 1

-16ab+8(a+b)²=-16ab+8(a²+2ab+b²)=
=8(a²+b²)=8((✓2)²+(✓5)²)=8•(2+5)=8•7=56

Answer 2

To evaluate the expression -16ab + 8(a + b)^2 when a = √2 and b = √5, we just need to substitute the given values into the expression and perform the calculations step by step.

Step 1: Substitute the values of a and b into the expression.

-16ab + 8(a + b)^2 = -16(√2)(√5) + 8(√2 + √5)^2

Step 2: Simplify the terms inside the parentheses.

-16(√2)(√5) = -16√10

Step 3: Expand the square of the binomial (√2 + √5)^2.

(√2 + √5)^2 = (√2)^2 + 2(√2)(√5) + (√5)^2 = 2 + 2√10 + 5 = 7 + 2√10

Step 4: Substitute the value back into the original expression.

-16ab + 8(a + b)^2 = -16√10 + 8(7 + 2√10)

Step 5: Distribute the 8 into the parentheses.

-16√10 + 8(7 + 2√10) = -16√10 + 56 + 16√10

Step 6: Combine like terms.

-16√10 + 16√10 = 0

Step 7: Final answer.

-16ab + 8(a + b)^2 = 0

So, when a = √2 and b = √5, the expression -16ab + 8(a + b)^2 evaluates to 0.