Quadratic formula is x=(-b+-sqrt(b^2-4ac))/(2a)
a= 1, b=-4, and c=3
Therefore, x=(-(-4)+-sqrt((-4)^2-4(1)(3))/(2(1))
Solve for both the plus and minus equations; the answers will be the roots to the quadratic equation.
Answer:
(1,2)
y=2
x=1
Step-by-step explanation:
x+y=3
3x+5y=13
solve the equation
x=3-y
3x+5y=13
substitute the value of x into an equation
3(3-y)+5y=13
distribute
9-3y+5y=13
add -3y to 5y
9+2y=13
subtract 9 from both sides
2y=4
divide both sides by 2
y=2
substitute the value of y into an equation
x=3-2
subtract 3 to 2
x=1
--------
(1,2)
--------
Answer:
Step-by-step explanation:
x + 7 < 4
x < 4 - 7
x < -3
Answer:
Step-by-step explanation:
The numbers are 11 & 12
Explanation:
Let the first number be f and the second |number be s
Now the square of first No. is 23 less than the square of second No.
ie. f
2
+
23
=
s
2
. . . . . (1)
The second No. is 1 more than the first
ie f
+
1
=
s . . . . . . . . . . .(2)
squaring (2), we get
(
f
+
1
)
2
=
s
2
expanding
f
2
+
2
⋅
f
+
1
=
s
2 . . . . . (3)
Now (3) - (1) gives
2
⋅
f
−
22
=
0
or
2
⋅
f
=
22
thus, f
=
22
2
=
11
and s
=
f
+
1
=
11
+
1
=
12
So the numbers are 11 & 12
