[The question's not wholly right! Since, (a+b) has a and b in it, it already is in terms of a and b. Here, we'll be representing (a+b) in terms of ab]
Answer:
[tex]\mathsf{\sqrt{10ab} }[/tex]
Step-by-step explanation:
We have the rules of indices, one of which is:
[tex]\boxed{\large{\mathfrak{(a+b)^2=a^2+b^2+2ab}}}[/tex]
Indices are the powers, the numbers written as superscript in front of a variable or the numbers that come along with "^". It shows how many times a number is to be multiplied by itself.
In the question, we're provided with one equation, i. e.,
- a² + b² = 8ab . . . . . . . . (¡)
And, were asked to find out the value of (a+b) in terms of ab.
The above rule has variables that fit in the question efficiently!
So, instead of solving for (a+b), we'll be solving for (a+b)², then go for (a + b):
=> (a + b)² = (a² + b²) + 2ab
from eqn. (¡):
=> (a + b)² = 8ab + 2ab
=> (a + b)² = 10ab
taking under root on both the sides:
=> (a + b) = [tex]\mathsf{\sqrt{10ab} }[/tex]
That's the answer, [tex]\mathsf{\sqrt{10ab} }[/tex]!
[tex]\overline{\mathfrak{Hope \:this \:makes\: sense!}}[/tex]
