corresponding angles, therefore
m∠1 = m∠2 → m∠2 = 130°
vertical angles, therefore
m∠2 = m∠3 → m∠3 = 130°
If ∠1 and ∠2 are complementary, then m∠1 + m∠2 = 90°.
If ∠2 and ∠3 are complementary, then m∠2 + m∠3 = 90°
Therfore
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
The answer is B.
If you find a common denominator, the process becomes much easier. I hope this was helpful.
72 because right number on the top of the bar is six, and 12•6=72
<span> r+5 </span><span>r^2+4r-21
</span><span>-------------- / --------------------
r^2+5r-14 </span><span>r-2
</span> r+5 r-2
= -------------- x --------------------
r^2+5r-14 r^2+4r-21
r+5 r-2
= -------------- x --------------------
(r+7)(r-2) (r+7)(r-3)
r+5
= -----------------
(r+7)^2 (r-3)
