Question

(√m + √5)² - (m+5) пж​

Answer 1

По формуле квадрата суммы:

$(x + y) {}^{2} = {x}^{2} + 2xy + {y}^{2} \\ ( \sqrt{m} + \sqrt{5} ) {}^{2} = ( \sqrt{m} ) {}^{2} + 2 \sqrt{m} \sqrt{5} + ( \sqrt{5} ) {}^{2} = \\ = m + 2 \sqrt{5m} + 5$

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

Answer 2

Sure, I can help you simplify this expression.

Let's break it down step by step:

(√m + √5)² - (m + 5)

First, let's expand the square of the binomial (√m + √5)²:

(√m + √5)² = (√m)² + 2(√m)(√5) + (√5)² = m + 2√(5m) + 5

Now, we can rewrite the expression:

m + 2√(5m) + 5 - m - 5

Next, we can simplify further:

2√(5m)

That's the simplified form of the expression (√m + √5)² - (m + 5). If you have a specific value for 'm', you can substitute it in to get a numerical result.