Question

(а -1)² - (2а + 9)² = 0

Answer 1

A2-2a+1-4a2-36a-81=0
-3a2-38a-80=0 /*-1
3a(a+10)+8(a+10)=0
(a+10)(3a+8)=0
a=-10
a=-8/3

Answer 2

Ответ:

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Answer 3

To solve the equation (a - 1)² - (2a + 9)² = 0, we can simplify it and then factor it.

Let's expand the square terms first:

(a - 1)² = (a - 1)(a - 1) = a² - 2a + 1 (2a + 9)² = (2a + 9)(2a + 9) = 4a² + 36a + 81

Now we substitute these expressions back into the equation:

(a - 1)² - (2a + 9)² = 0 (a² - 2a + 1) - (4a² + 36a + 81) = 0

Now distribute the negative sign in front of the second parentheses:

a² - 2a + 1 - 4a² - 36a - 81 = 0

Combine like terms:

-3a² - 38a - 80 = 0

To factor the quadratic equation, we look for two numbers whose product is -3 * -80 = 240 and whose sum is -38. After considering various pairs of factors of 240, we find that -40 and +6 satisfy these conditions.

Therefore, we can rewrite the equation as:

(-3a + 6)(a + 40) = 0

Setting each factor equal to zero gives us two separate equations:

-3a + 6 = 0 or a + 40 = 0

Solving each equation gives us:

-3a = -6 or a = -40

Dividing both sides of the first equation by -3:

a = 2

Therefore, the solutions to the equation (a - 1)² - (2a + 9)² = 0 are:

a = 2 and a = -40.