Question

69-(13-у)степ2=-у степ2

Answer 1

Здравствуйте!

Вот ваше решение:

$69-(13-y)^{2} = -y^{2} \\69-(169-26y+y^{2} )=-y^{2} \\69-169+26y-y^{2}= -y^{2} \\69-169+26y = 0\\-100+26y = 0\\26y = 100\\y = \frac{50}{13} \\y = 3\frac{11}{13}$

Answer 2

Let's solve the equation step by step to find the value of у (pronounced as "u").

Given equation: 69 - (13 - у)² = -у²

Step 1: Expand the square term (13 - у)² (13 - у)² = (13 - у)(13 - у) = 13 * 13 - 13 * у - у * 13 + у * у = 169 - 26у + у²

Now, the equation becomes: 69 - (169 - 26у + у²) = -у²

Step 2: Remove the brackets: 69 - 169 + 26у - у² = -у²

Step 3: Combine the у² terms on one side: 26у - у² - у² = 69 - 169

Step 4: Simplify: 26у - 2у² = -100

Step 5: Set the equation to zero: 2у² - 26у - 100 = 0

Now, we have a quadratic equation in terms of у. To solve for у, we can use the quadratic formula:

The quadratic formula is given by: у = (-b ± √(b² - 4ac)) / 2a

Where a, b, and c are the coefficients of the quadratic equation (ay² + by + c = 0).

In our case, a = 2, b = -26, and c = -100. Plugging these values into the quadratic formula:

у = (26 ± √((-26)² - 4 * 2 * -100)) / 2 * 2

у = (26 ± √(676 + 800)) / 4

у = (26 ± √1476) / 4

Now, we have two possible solutions for у:

1. у = (26 + √1476) / 4
2. у = (26 - √1476) / 4

Calculating the values:

1. у ≈ (26 + 38.43) / 4 ≈ 16.43
2. у ≈ (26 - 38.43) / 4 ≈ -3.43

So, the two possible solutions for у are approximately 16.43 and -3.43.