Question
Simplify: (√5 + √3)/(√5 − √3) + (√5
− √3)/(√5 + √3)Solution
Let a = √5, b = √3. Expression = (a + b)/(a − b) + (a − b)/(a + b) = [(a + b)² + (a − b)²] / (a² − b²) (a + b)² = a² + 2ab + b² (a − b)² = a² − 2ab + b² Sum = 2a² + 2b² Denominator = a² − b² So expression = 2(a² + b²)/(a² − b²) Now a² = 5, b² = 3: = 2(5 + 3)/(5 − 3) = 2×8/2 = 8.
251, 130, 274, ?, 301, 76
14, 17, 23, 32, ?, 59
18, 30, 54, 90, 138, ?
What will come in place of the question mark (?) in the following series?
18, 22, 34, 70, 178, ?
7 4 5 9 20 ? 160.5
4, 4, 12, 60, ?, 3780
12, 14, 20, 32, ?, 82
What will come in place of the question mark (?) in the following series?
45, 68, 114, 183, 275, ?
What will come in place of the question mark (?) in the following number series?
21, 42, 67, 96, ?, 166
What will come in place of the question mark (?) in the following series?
4, 2605, 5309, 8118, ?
