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The positive value of k for which x2 +Kx +64 = 0 & x2 - 8x + k = 0 will have real roots .
Ans: x2 + Kx + 64 = 0
⇒ b2 -4ac > 0
K2 - 256 > 0
K > 16 or K < - 16 ...............(1)
x2 - 8x + K = 0
64 - 4K > 0
⇒ 4K < 64
K < 16 ...............(2) From (1) & (2) K = 16
A two-digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the original number. Find the original number.
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