Question
Simplify the expression: (√7 + √5)/(√7 −
√5) + (√7 − √5)/(√7 + √5)Solution
Let a = √7, b = √5. 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 = 7, b² = 5: = 2(7 + 5)/(7 − 5) = 2×12 / 2 = 12.
The speed of a boat in still water is 10 kmph. It covers a distance of 60 km downstream in 5 hrs. The speed (in kmph) of the stream is
A boat can cover 140 km in downstream in 7 hours and 130 km in upstream in 13 hours. Find the speed of boat in still water.
Speed of a boat in still water to speed of boat in upstream is 7:5. If the boat can travel 360 km in downstream in 5 hours, then find the time taken by ...
A boat takes a third time to cover a certain distance downstream compared to upstream. What is the ratio of the speed of the boat in still water to the ...
A boat goes 200 km with the current in 10 hours, and returns the same distance against the current in 20 hours. Find the speed of the boat in still water.
A boat running downstream covers a distance of 45 km in 9 hrs and covering the same distance upstream in 15 hrs. What is the speed of a boat in still wa...
If a man rows at the rate of 19 kmph in still water and his rate against the current is 7 kmph, then find the man’s speed with downstream. ...
The ratio of the speed of boat ‘A’ in still water, the speed of boat ‘B’ in still water and the speed of the current is 8:6:2, respectively. If ...
A boat can cover 143 km in downstream in 11 hours and 120 km in upstream in 12 hours. Find the speed of boat in still water
When travelling downstream, a boat takes 4.25 hours to travel 187 km. If the speed of the stream is (5/11)th of downstream speed of the boat,...
