the value of (a+b)² if a= 7 and b = -5 is__________.
Answers
Answer:
(a−b)2 expands to a2–2ab+b2, which equals 7.
We know that ab equals 14, so substitute it into the above equation.
a2–28+b2=7
a2+b2=35
Now for some creativity. a2+b2 is the “newbie” answer to the expansion of (a+b)2: i.e. with the midsection missed out:
(a+b)2=a2+2ab+b2
Now we know that a2+b2=35 and 2ab=28, so add the two together to get (a+b)2=a2+2ab+b2=35+28=63
Therefore (a+b)2=63. Now to find out a and b’s vaaaalyeeeews. By rooting both sides we can see that a+b=±37–√.
Notice that having both a+b and ab is the “product/sum” stage of a basic quadratic factorisation: (x+a)(x+b)=x2+(a+b)x+ab
So now we can use the quadratic formula to filter out our solutions.
x=∓37–√±(37–√)2−(4×1×14)−−−−−−−−−−−−−−−−−√2
x=∓37–√±63–56−−−−−√2
x=∓37–√±7–√2
You’ll end up with the following solutions:
x=7–√,27–√
and
x=−7–√,−27–√
But b>0, so...
Our final answer: a and b are 7–√ and 27–√. In either order.
Answer:
(a+b)²
For a=7,b=-5
{7+(-5)}²
=(2)²
=4