Question

Найдите значение выражения (5+√2)²+(5-√2)²

Answer 1

$\displaystyle\bf\\\Big(5+\sqrt{2} \Big)^{2} +\Big(5-\sqrt{2} \Big)^{2} =5^{2} +2\cdot 5\cdot \sqrt{2} +(\sqrt{2} )^{2} +5^{2} -2\cdot 5\cdot \sqrt{2} +(\sqrt{2} )^{2} =\\\\\\=25+10\sqrt{2} +2+25-10\sqrt{2} +2=54\\\\\\Otvet: \ 54$

Answer 2

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To find the value of the expression $(5+\sqrt{2})^2+(5-\sqrt{2})^2$, we can use the formula for the square of a binomial: $(a+b)^2=a^2+2ab+b^2$. Applying this formula to each term, we get:

$(5+\sqrt{2})^2+(5-\sqrt{2})^2=(5^2+2\cdot 5\cdot \sqrt{2}+(\sqrt{2})^2)+(5^2-2\cdot 5\cdot \sqrt{2}+(\sqrt{2})^2)$

Simplifying, we get:

$= (25+10\sqrt{2}+2)+(25-10\sqrt{2}+2)$

$= 50+4+0$

$= 54$

Therefore, the value of the expression is 54. You can also use online tools to check your answer or get step-by-step explanations.

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