Question

Известно что a+b=7 ab=6 найдите значение выражения a^2+b^2

Answer 1

Ответ:

72,37,2

Объяснение:

Смотри на фото:

Answer 2

Ответ:

37

Объяснение:

а = 7-b

(7-b)b = 6

7b - b^2 = 6

-b^2+7b-6 = 0 |:(-1)

b^2-7b+6=0

1-7+6=0

b=1; b=6

b=6 b=1

a+6=7 a+1=7

a=1 a=6

6×1= 7 1×6=7

6^2+1^2=36+1=37

Answer 3

To find the value of the expression a^2 + b^2, we need to first determine the individual values of 'a' and 'b' using the given information. We are given two equations:

1. a + b = 7
2. ab = 6

Let's solve for 'a' and 'b' using these equations:

From equation 1, we can express 'a' in terms of 'b': a = 7 - b

Now, substitute this expression for 'a' into equation 2: (7 - b) * b = 6

Expand the equation: 7b - b^2 = 6

Rearrange the equation: b^2 - 7b + 6 = 0

Now, factorize the quadratic equation: (b - 6)(b - 1) = 0

Setting each factor to zero and solving for 'b': b - 6 = 0 -> b = 6 b - 1 = 0 -> b = 1

Now that we have two possible values for 'b', let's find the corresponding values of 'a':

When b = 6: a = 7 - b = 7 - 6 = 1

When b = 1: a = 7 - b = 7 - 1 = 6

So, the two possible pairs of 'a' and 'b' that satisfy the given equations are (a = 1, b = 6) and (a = 6, b = 1).

Now, let's calculate the value of the expression a^2 + b^2 for both pairs:

1. For a = 1 and b = 6: a^2 + b^2 = 1^2 + 6^2 = 1 + 36 = 37

2. For a = 6 and b = 1: a^2 + b^2 = 6^2 + 1^2 = 36 + 1 = 37

So, the value of the expression a^2 + b^2 is 37, regardless of which pair of values (a, b) we choose.