Question

Известно что a-b=6, ab=-5. найдите значение выражения (a+b)^2​

Answer 1

Ответ:16

Пошаговое объяснение:

{a-b=6,

{ab=-5

{а=b+6

{(b+6)b=-5

(b+6)b=-5

b²+6b+5=0

D=6²-4*5=36-20=16=4²

1)b=(-6+4)/2=-1;

2)b=(-6-4)/2=-5

1)

{b=-1

{a=-1+6

{b=-1

{a=5

(a+b)²=(5-1)²=4²=16

2)

{b=-5

{a=-5+6

{b=-5

{a=1

(a+b)²=(1-5)²+(-4)²=16

Answer 2

To find the value of the expression (a+b)^2, we can use the formula for squaring a binomial:

(a + b)^2 = a^2 + 2ab + b^2

Given that a - b = 6 and ab = -5, we can use these equations to find the values of a^2 and b^2:

(a - b)^2 = a^2 - 2ab + b^2 (6)^2 = a^2 - 2(-5) + b^2 36 = a^2 + 10 + b^2

Now, let's try to find the values of a^2 and b^2 separately.

Step 1: Solve for a^2 a^2 = 36 - 10 - b^2

Step 2: Substitute the value of ab into the equation to find b^2 ab = -5 a * b = -5 b = -5 / a

Substitute b = -5 / a into the equation a^2 + 10 + b^2 = 36

a^2 + 10 + (-5 / a)^2 = 36 a^2 + 10 + 25 / a^2 = 36

Step 3: Now, multiply the entire equation by a^2 to eliminate the fraction:

a^2 * (a^2 + 10 + 25 / a^2) = a^2 * 36 a^4 + 10a^2 + 25 = 36a^2

Step 4: Move all terms to one side of the equation:

a^4 + 10a^2 - 36a^2 + 25 = 0 a^4 - 26a^2 + 25 = 0

Step 5: Factor the quadratic equation:

(a^2 - 25)(a^2 - 1) = 0

Step 6: Solve for a:

a^2 - 25 = 0 or a^2 - 1 = 0

If a^2 - 25 = 0: a^2 = 25 a = ±√25 a = ±5

If a^2 - 1 = 0: a^2 = 1 a = ±√1 a = ±1

So, we have four possible values for 'a': a = 5, a = -5, a = 1, or a = -1.

Step 7: Find the corresponding values of 'b' using the equation ab = -5:

If a = 5: b = -5 / 5 b = -1

If a = -5: b = -5 / -5 b = 1

If a = 1: b = -5 / 1 b = -5

If a = -1: b = -5 / -1 b = 5

Now that we have all possible values of 'a' and 'b', let's calculate the value of (a+b)^2 for each case:

If a = 5 and b = -1: (a + b)^2 = (5 + (-1))^2 = 4^2 = 16

If a = -5 and b = 1: (a + b)^2 = (-5 + 1)^2 = (-4)^2 = 16

If a = 1 and b = -5: (a + b)^2 = (1 + (-5))^2 = (-4)^2 = 16

If a = -1 and b = 5: (a + b)^2 = (-1 + 5)^2 = 4^2 = 16

The value of (a + b)^2 is 16 for all four cases.