X is 7 more than y
x>y then
difference betwen squares is 161 so
x=7+y
and
x²-y²=161
so
x=7+y
sub that for x in other equation
(7+y)²-y²=161
y²+14y+49-y²=161
14y+49=161
minus 49 both sides
14y=112
divide both sides by 14
y=8
sub back
x=7+y
x=7+8
x=15
the numbers are 15 and 8
The answer is D. (2.9,-22.8)
Answer:
x²-8x-1=0
comparing above equation with ax²+bx+c=0
a=1
b=-8
c=-1
x=

=(--8+-√(64-4×1×-1)/2×1
=8+-√(64+4)/2
taking positive
x=(8+√68)/2=2(4+√17)/2=4+√17
taking negative
x=(8-√68)/2=2(4-√17)/2=4-√17
9514 1404 393
Answer:
"complete the square" to put in vertex form
Step-by-step explanation:
It may be helpful to consider the square of a binomial:
(x +a)² = x² +2ax +a²
The expression x² +x +1 is in the standard form of the expression on the right above. Comparing the coefficients of x, we see ...
2a = 1
a = 1/2
That means we can write ...
(x +1/2)² = x² +x +1/4
But we need x² +x +1, so we need to add 3/4 to the binomial square in order to make the expressions equal:

_____
Another way to consider this is ...
x² +bx +c
= x² +2(b/2)x +(b/2)² +c -(b/2)² . . . . . . rewrite bx, add and subtract (b/2)²*
= (x +b/2)² +(c -(b/2)²)
for b=1, c=1, this becomes ...
x² +x +1 = (x +1/2)² +(1 -(1/2)²)
= (x +1/2)² +3/4
_____
* This process, "rewrite bx, add and subtract (b/2)²," is called "completing the square"—especially when written as (x-h)² +k, a parabola with vertex (h, k).