a^2- ab+b^2= if a+b= 10 and ab=18
Answers
Answer:
As we know,
(a-b)^2=a^2+b^2–2ab
==>a^2+b^2=(a-b)^2+2ab———→(1)
(a+b)^2=a^2+b^2+2ab
on substituting eq(1) in above eq
(a+b)^2=(a-b)^2+4ab
(a+b)^2=(8)^2+4(9) as per in the question
(a+b)^2=64+36
(a+b)^2=100
by taking square on both sides
s0 a+b=10
a-b=8
a=8+b
ab=9
Therefore if a=8+b
(8+b)b=9
8b + b^2=9
b^2+8b-9=0
(b+9)*(b-1))=0
Therefore b=-9 OR b=1
If b=-9
a=8–9=-1
If b=1
a=8+1=9
Therefore a+b=9+1=10
OR
a+b=-1–9=-10
As a-b=8,ab=9
a=8+b
(8+b)b=9
8b+b^²=9
Solve the eqn using quadratic equationan u get
You get b^²+8b-9=0
So by solving we get
b=—9,+1.
a=8+(—9,1)
a=—1,9
a+b=—9–1=—10
1+9=10.
(a-b)^2 =a^2+b^2 -2ab
8x8=a^2+b^2 -2x9
64+18=a^2+b^2
So, a^2+b^2=82
Now,
(a+b)^2=a^2+b^2+2ab
(a+b) =√100
So a+b =10 {Ans}
(a+b)² = a² + 2ab + b² , and
(a - b)² = a² - 2ab + b² , so
(a + b)² = (a - b)² + 4ab
so, According to your question,
(a + b)² = 8² + 4 x 9 = 64 + 36 =
thus, a + b = √(100) = 10
I hope this helps
We are given that,
a-b=8
ab = 9
Now,
(a-b)² = a²+b² - 2ab
(8)²= a²+b² - 2(9)
64= a²+b² -18
64+18= a²+b²
a²+b²=82
Now,
(a+b)²= a²+b²+2ab
(a+b)²=82+2(9)
(a+b)²=82+18
(a+b)²=100
√{(a+b)²}=√100
a+b=+_10 (+ve, -ve 10)
It seems to be too simple.
The two numbers a & b are 9 & 1 respectively.
a - b = 8
9 - 1 = 8
Proved by trial and error method. No logic needed the amount was too small to assume hence.
Hope so the content was useful & Worthy.
As a-b= 8
=> a=8+b
ab =9
(8+b)b =9 {from above equations}
8b +b^2 =9
on solving this quadratic equation :
b=-9,1
so -9 and 1 is the answer
We will think of the numbers that if we multiply give the answer 9. These are 3 and 3, 9 and 1. We can see that if we subtract 9 and 1 we get 8. So, with 9 and 1 both the conditions are satisfied. a = 9 and b = 1. So, 9+1 will be 10.
Answer is 10
a-b=8
a=8+b…….(1)
ab=9
put value of a in above equation
(8+b)b=9
b²+8b-9=0………..[quadratic equation]
i.e b²+9b-b-9=0
b(b+9)-1(b+9)=0
(b-1)(b+9)=0
∴ b-1=0 or b+9=0
b=1 or b=-9
Its a rule to only take the positive one.
So taking b=1
a-b=8
So—a-1=8
Then a=9
So a+b=9+1=10.
The answer is 10.
Here,
a-b = 8 and ab = 9 —————(i)
As we know that (a-b)^2 = (a+b)^2 - 4(ab) ———(ii)
We have use this equation (ii) we get,
(8)^2 = (a+b)^2 - 4(9) {from equation (i)}
64 = (a+b)^2 - 36
(a+b)^2 = 64 + 36
(a+b)^2 = 100
(a+b) = +10 & -10 —————-(iii)
Hence, (a+b) = +10 &-10
We also find the value of a & b by using equati
Answer:
answer for the given problem is given
