Question

-10ab+5(a+b)^2 при a = 2√3 при b = √5

Answer 1

-10аb+5(a^2+2ab+b^2)=-10ab+10ab+5a^2+5b^2=5a^2+5b^2=5x12+5x5=60+25=85

Answer 2

To evaluate the expression -10ab + 5(a + b)^2 with a = 2√3 and b = √5, we substitute the given values into the expression and perform the necessary calculations.

Let's substitute a = 2√3 and b = √5 into the expression:

-10ab + 5(a + b)^2 = -10(2√3)(√5) + 5((2√3) + (√5))^2

Now, let's simplify the expression step by step:

-10(2√3)(√5) = -10(2)(√3)(√5) = -40√15

((2√3) + (√5))^2 = (2√3 + √5)(2√3 + √5) = (2√3)^2 + 2(2√3)(√5) + (√5)^2 = 12 + 4√15 + 5 = 17 + 4√15

Substituting these values back into the expression:

-10ab + 5(a + b)^2 = -40√15 + 5(17 + 4√15) = -40√15 + 85 + 20√15 = 45 + (-40 + 20)√15 = 45 - 20√15

Therefore, the value of the expression -10ab + 5(a + b)^2 when a = 2√3 and b = √5 is 45 - 20√15.