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ax²+bx+c=ax²+ap²-2apx
b=-2ap=> b²=4a²p²
c=ap²
b²=4a²*c/a
b²=4ac

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1) 24*24, 18*18, 12*12, 6*6, 6*6

2) min HCF(24,42) = 6

24*42/6*6 = 28

5:28

m + n - 1 = 2mn/5

5m + 5n - 2mn = 5

(2m - 5)(2n - 5) = 15

15 == 1*15, 3*5, 5*3, 15*1

Compare and solve for m,n

(x - 1)² + (y - 3)² = r²

(x - 4)² + (y + 1)² = 3²

Distance between centres = 5

So if r = 2 they will touch each other externally

So r > 2

And if r = 8

They will touch each other internally
r < 8

2 < r < 8

r = 2,3,4,5,6,7

(x² - x - 6)(x² - x - 20) + 40

(x² - x - 13 + 7)(x² - x - 13 - 7) + 40

(x² - x - 13)² - 49 + 40

(x² - x - 16)(x² - x - 10)

Number = 5(6(7x + 5) + 4) + 2

= 210x + 172 is a multiple of 8

Put values of x and check if it is multiple of 8 or not

x = 2 , number = 592

x = 6, number = 1432

11

52*7 = 364

364*11 + 52 = 4056

4056*2 + 364 = 8476

(4056, 8476)