X² + 1 = 0
=> (x+1)² - 2x = 0
=> x+1 = √(2x)
or x - √(2x) + 1 = 0
Now take y=√x
So, the equation changes to
y² - y√2 + 1 = 0
By quadratic formula, we get:-
y = [√2 ± √(2–4)]/2
or √x = (√2 ± i√2)/2 or (1 ± i)/√2 [by cancelling the √2 in numerator and denominator and ‘i' is a imaginary number with value √(-1)]
or x = [(1 ± i)²]/2
So roots are [(1+i)²]/2 and [(1 - i)²]/2
Thus we got two roots but in complex plane. If you put this values in the formula for formation of quadratic equation, that is x²+(a+b)x - ab where a and b are roots of the equation, you will get the equation
x² + 1 = 0 back again
So it’s x=1 or x=-1
Answer:
=6√3 the third option.
Step-by-step explanation:
We can use the Pythagoras theorem to find the value of y. We need two equations that include y.
a²+b²=c²
c=9+3=12
x²+y²=12²
x²=144 - y².........i (This is the first equation)
We can also express it in another way but let us find the perpendicular dropped to c.
perpendicular²= x²-3²=x²-9 according to the Pythagoras theorem.
y²=(x²-9)+9²
y²=x²+72
x²=y²-72....ii( this is the second equation
Let us equate the two.
y²-72=144-y²
2y²=144+72
2y²=216
y²=108
y=√108
In Surd form √108=√(36×3)=6√3
y=6√3
Answer:
325 employees
Step-by-step explanation:
men to women is
8:5
125/5 is 25
8*25=200
200+125=325
325 employees
75% = 3/4
3/4 of 180 = 135
Answer:
π/8
Step-by-step explanation:
Phase shift = c/b
= (π/2) / 4
= π/8
