help me plzzz!!algebra question!?

Question

if a+b=9
and ab=7
then a^2+b^2=?

Answer 1

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

We've got ab, so 2ab=14.
(a+b)^2=9^2=81
We can say that:

a^2+ b^2=(a+b)^2 -2ab
a^2+ b^2=81-14
a^2+b^2=67


Pretty simple, don't you think?? All you have to know is this binomial identity. The person who invented this question wanted to see if the students knew their identities. HoHOHoHoHoHO!!!!!!!

Answer 2

use the formula (a + b)^2 = a^2 + 2ab + b^2

so 9^2 = a^2 + b^2 + 2 x 7

81 = a^2 + b^2 + 14

a^2 + b^2 = 81 - 14
= 67

Answer 3

a + b = 9

ab = 7

If you square both sides of the first equation you get...

(a+b)² = 9² or (a +b)² = 81

(a+b)² = (a² + 2ab + b²) therefore

(a² + 2ab + b²) = 81

since ab = 7

(a² + 2(7) + b²) = 81 or (a² + 14 + b²) = 81

subtract 14 from both sides and get

(a² + b²) = 67

and there's you answer.

Answer 4

(a+b)^2 = 9^2
(a+b)^2 = 81


Since (a+b)^2 = a^2 + 2ab + b^2
81 = (a^2 + b^2) + 2(7)
81-14 = a^2 + b^2
67 = a^2 + b^2

Answer 5

a + b =9
(a + b)^2 = 9^2
a^2 +b ^2 +2ab = 81
a^2 +b^2 + 2(7) =81
a^2 +b^2 + 14 =81
a^2 +b^2 =81 - 14
a^2 +b^2 = 67

Answer 6

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

(a+b)^2=9^2
=81
ab=7
Therefore, a^2+b^2 =81-(2*7)
=81-14
=67
Answer : 67

Answer 7

a^2+b^2
=(a+b)^2-2ab
=9^2-2*7
=81-14
=67

Answer 8

the solution is horrible dude

the roots that u get r also horrible

wat u do is

a+b=9
a=9-b

(9-b)b=7

solve the quadratic equation n get the value of b

substitute value of b in a+b=9

u get values of a and b

hence u get ur answer for the question

Answer 9

a = 9 - b
b = 9 - a

b(9 - b) = 7
b^2 + 9b - 7 = 0

a,b = 8.14, 0.86

a^2+b^2 = 67

Answer 10

we are that given a+b=7, and ab=7
(a+b)^2=a^2+b^2+2ab
a^2+b^2=(a+b)^2-2ab
a^2+b^2=(9)^2-2*7
a^2+b^2=18-14
a^2+b^2=4