If the cost of 2 apples, 3 oranges and a pear is Rs.62 and the cost of 5 apples, 6 oranges and 4 pears is Rs. 120, then find the cost of 3 apples, 3 oranges and 3 pears?

Let Arjun had x arrows.
? x/2 + 6 + 3 + 4?x + 1 = x
? x = 20 + 8?x
? x - 20 =8?x
On squaring both sides and by solving the formed quadratics equation, we get x = 100

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

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

According to question ,
PQ = ?( 5 - 2 )² + ( 4 - 0 )²
PQ = ?9 + 16 = 5
? Area of circle = ?r²
Area of circle = 25 ? sq. units