What is the following product? (x square root 7 - 3 square root 8) (x square root 7 - 3 square root 8)

Mathematics

2 answers:

bogdanovich [222]3 years ago

8 0

Answer:

7x^2 -6x√56 + 72

Step-by-step explanation:

(x√7 - 3√8)(x√7 - 3√8) ➡ (x√7 - 3√8)^

x^2 × 7 - 3x√56 - 3x√56 + 9×8 ➡ 7x^2 -6x√56 + 72

Semmy [17]3 years ago

3 0

Answer:

7 x² - 6 x √56 +72

Step-by-step explanation:

Let's consider the following equation.

(x√7 - 3√8).(x√7 - 3√8)

This is equal to a squared binomial.

(x√7 - 3√8)²

This is equal to the square of the first term, minus the double of the product of the first by the second plus the square of the second term.

(x√7)² - 2 × x√7 × 3√8 + (3√8)²

7 x² - 6 x × √(7.8) + 9 . (√8)²

7 x² - 6 x √56 +72

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Use the definition of the derviative to compute the derivative of f(x)= 1- 7x^2 at the specific point x=2.

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Answer:

$f'(x) = -28 \ at \ x = 2$

Step-by-step explanation:

$f'(2) = \lim_{h \to 0}\frac{f(2+h)) -f(2)}{h} \\\\f(2+h) = 1 - 7(2+h)^2 = 1 - 7(4 +h^2 +4h) = 1 - 28 - 7h^2 - 28h = - 7h^2 -28h - 27\\\\f(2) = 1 - 7(2^2) = 1 - 28 = -27\\\\f(2+h) - f(2) = -7h^2 - 28h - 27 - (-27) = -7h^2 -28h -27 + 27 = -7h^2 -28h\\\\f'(2) = \lim_{h \to 0}\frac{-7h^2 - 28h}{h} \\\\$