Question

Не выполняя вычислений сравните значение выражений 1875^2+1876^2 и (1875+1876)^2

Answer 1

Ответ:

(1875+1876)² больше

Объяснение:

(1875+1876)²=1875²+2×1875×1876+1876²

1875²+1876²<(1875+1876)²

Answer 2

To compare the values of the expressions without performing the actual calculations, we can use a property of algebra called the distributive property.

The distributive property states that for any real numbers a, b, and c:

(a + b)^2 = a^2 + 2ab + b^2

Now, let's apply this property to the expression (1875 + 1876)^2:

(1875 + 1876)^2 = 1875^2 + 2 * 1875 * 1876 + 1876^2

As we can see, the expression (1875 + 1876)^2 contains an additional term 2 * 1875 * 1876 compared to 1875^2 + 1876^2.

Since 1875 and 1876 are close to each other, their product 2 * 1875 * 1876 will be relatively small compared to the squares of these numbers.

Thus, we can conclude that (1875 + 1876)^2 will be greater than 1875^2 + 1876^2.