Angry Arjun carried some arrows for fighting with Bheshhm. With half the arrows, he cut down the arrows thrown by Bheeshm on him and with six other arrows he killed the rath driver of Bheeshm. with one arrows each he Knocked down respectively the rath, flag and the bow of Bheeshm. Finally, with one more than four times the square root of arrow he laid Bheeshm unconscious on an arrow bed. What is the total number of arrows Arjun had?

According to question , we have
?( x - 0 )² + ( 0 + 5 )² = 13
? x² + 25 = 169
? x² = 169 - 25 = 144
? x = ?144 = 12

Let the cost of each apple,orange nd pear be Rs.x,y and z, respectively.Then,
2x + 3y + z = 62 ...(i)
5x + 6y + 4z = 20 ...(ii)
On subtracting Eq.(i)from Eq.(ii), we get
3x + 3y + 3z = 58
So, the cost of 3 apple,3 oranges and 3 pears is Rs. 58.

When p is wrong i.e., -b/a = (? + ?) is wrong but c/a =(??) is correct.
Then ?? = c/a = 2 x 6 = 12 ....(i)

Again, when q is wrong i.e.,c/a = (?.? ) is wrong but -b/a = ?+? is correct.
Then, -b/a = ?+?= 2 + (-9) = -7

So, the required correct quadratic equations is
x² -(? + ?)x + ?.?=0
? x² - (-7)x + 12 = 0
? x² + 7x + 12 = 0
and correct roots this equations are -3, -4.

As we know from the formula,
A³ + B³ + C³ = ( A + B + C) (A² + B² + C² ? AB ? BC ? CA) + 3ABC
If A + B + C = 0 then,
A³ + B³ + C³ = 0 x (A² + B² + B² ? AB ? BC ? CA) + 3ABC
A³ + B³ + C³ = 0 + 3ABC
A³ + B³ + C³ - 3ABC= 0
As we know that from given question,
A = a, B = b and C = 1, Put these value in above equation, we will get
a³ + b³ + 1³ - 3 x a x b x 1 = 0
a³ + b³ + 1 - 3ab = 0

As we know that given in question,
ax + by = 6 ........................ (i)
bx ? ay = 2 ........................ (ii)
On squaring the both equation and adding,
a² x² + b² y² + 2abxy + b² x² + a² y² ? 2abxy = 36 + 4
? x² (a² + b²) + y² (a² + b²) = 40
? (a² + b²) (x² + y²) = 40
As per given question, x² + y² = 40 , Put this value in above equation, we will get
? (a² + b²) × 4 = 40
? a² + b² = 10