if a+b =7 and ab=12 , find 3(apower 2 - ab + b power 2)
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Answers
Answer:
13 is the value of \bold{a^2-ab+b^2}a
2
−ab+b
2
Given:
\begin{gathered}a+b=7 \\ab=12\end{gathered}
a+b=7
ab=12
To find:
The value of a^2-ab+b^2=?a
2
−ab+b
2
=?
Solution:
From the given
\begin{gathered}a+b=7 \\ab=12\end{gathered}
a+b=7
ab=12
To find the value of a^2-ab+b^2a
2
−ab+b
2
first express the term in to value given and then substitute the values and simplify it.
The value of the term a^2-ab+b^2a
2
−ab+b
2
can be found.
a^2-ab+b^2=a^2+2ab-3ab+b^2a
2
−ab+b
2
=a
2
+2ab−3ab+b
2
Using the identity \bold{a^2+2ab+b^2=(a+b)^2}a
2
+2ab+b
2
=(a+b)
2
=(a+b)^2-3ab=(a+b)
2
−3ab
Substituting the given value
\begin{gathered}=(7)^2-3(12)\\ =49-36=13\end{gathered}
=(7)
2
−3(12)
=49−36=13
Therefore, the value of\bold{a^2-ab+b^2}a
2
−ab+b
2
is 13. If a+b=7a+b=7 and ab=12.}
== (a+b)2=a2+b2+2ab
72=a2+b2+2(12)
a2+b2=49−24=25