Question

Вычислите(5+√3)^2-10√3

Answer 1

$(5+\sqrt{3} )^2-10\sqrt{3} =5^2+2*5*\sqrt{3} +(\sqrt{3} )^2-10\sqrt{3} =25+10\sqrt{3} +3-10\sqrt{3} =25+3=28$

Answer 2

To compute the expression, let's break it down step-by-step:

1. Start with (5 + √3)^2: (5 + √3)^2 = (5 + √3)(5 + √3)

2. Use the formula for the square of a binomial: (a + b)^2 = a^2 + 2ab + b^2 In this case, a = 5 and b = √3: (5 + √3)^2 = 5^2 + 2(5)(√3) + (√3)^2 = 25 + 10√3 + 3 = 28 + 10√3

3. Now subtract 10√3 from the result: (5 + √3)^2 - 10√3 = (28 + 10√3) - 10√3

4. The √3 terms will cancel out: (5 + √3)^2 - 10√3 = 28

So the final result is 28.