Question

(a-5)^2+2a(3a+5) при a=корень из 7 (можно подробно?)

Answer 1

$a {}^{2} - 10a + 25 + 6a {}^{2} + 10a = 7a {}^{2} + 25$

при а=корень из 7

$7 \times { \sqrt{7} }^{2} + 25 = 7 \times 7 + 25 = 49 + 25 = 74$

Answer 2

Sure, let's calculate the expression step by step with the given value of "a."

Given expression: (a-5)^2 + 2a(3a+5)

Substitute a = √7 into the expression:

Step 1: Calculate (a - 5)^2 Substitute a = √7: (√7 - 5)^2

Step 2: Calculate 2a(3a + 5) Substitute a = √7: 2√7(3√7 + 5)

Now, let's solve each part of the expression:

Step 1: (√7 - 5)^2

To expand the square, we can use the formula: (a - b)^2 = a^2 - 2ab + b^2

In this case, a = √7 and b = 5: (√7 - 5)^2 = (√7)^2 - 2(√7)(5) + (5)^2 = 7 - 2√7 * 5 + 25 = 7 - 10√7 + 25

Step 2: 2√7(3√7 + 5)

To multiply, use the distributive property: 2√7(3√7 + 5) = 2√7 * 3√7 + 2√7 * 5

To multiply √7 and 3√7, use the property √a * √b = √(a * b): 2√7 * 3√7 = 2 * 3 * √(7 * 7) = 6√49 = 6 * 7 = 42

Now, multiply the constants: 2√7 * 5 = 10√7

Step 2 result: 2√7(3√7 + 5) = 42 + 10√7

Now, let's put both results together and combine like terms:

(√7 - 5)^2 + 2√7(3√7 + 5) = (7 - 10√7 + 25) + (42 + 10√7)

Combine like terms: = 7 - 10√7 + 25 + 42 + 10√7

Now, the √7 terms cancel each other out: = 7 + 25 + 42

Finally, add all the constants together: = 74

So, the value of the expression (a-5)^2 + 2a(3a+5) when a = √7 is 74.