Question
The positions of how many digits in the number
‘457756893’ will remain unchanged after the digits are rearranged in ascending order within the number?Solution
4Â Â Â Â Â Â Â Â Â 5Â Â Â Â Â Â Â Â Â 7Â Â Â Â Â Â Â Â Â 7Â Â Â Â Â Â Â Â Â 5Â Â Â Â Â Â Â Â Â 6Â Â Â Â Â Â Â Â Â 8Â Â Â Â Â Â Â Â Â 9Â Â Â Â Â Â Â Â Â 3 3Â Â Â Â Â Â Â Â Â 4Â Â Â Â Â Â Â Â Â 5Â Â Â Â Â Â Â Â Â 5Â Â Â Â Â Â Â Â Â 6Â Â Â Â Â Â Â Â Â 7Â Â Â Â Â Â Â Â Â 7Â Â Â Â Â Â Â Â Â 8Â Â Â Â Â Â Â Â Â 9 So, there is no number, whose position remains unchanged.
I. 24x² - 58x + 23 = 0
II. 20y² + 24y – 65 = 0
I. 6x2 + 23x + 10 = 0
II. 2y2 - 3y - 5 = 0
I. p2 – 2p – 15 = 0
II. q2 + 4q – 12 = 0
Equation 1: x² + 16x + 63 = 0
Equation 2: y² + 10y + 21 = 0
Solve: x² − 7x + 12 = 0
I. 15y2 + 4y – 4 = 0
II. 15x2 + x – 6 = 0
I. x² + 4x + 4 = 0
II. y² - 8y + 16 = 0
I. 18p²- 21p + 6 = 0   Â
II. 16q² - 24q +9 = 0
I. 5x² - 24 x + 28 = 0  Â
II. 4y² - 8 y - 12= 0  Â
If x + 1/x = 3, find x² + 1/x².
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