The sum of two positive numbers is 27 and their product is 170. The positive difference between them is:
7
Let the two numbers be \(a\) and \(b\), with \(a + b = 27\) and \(ab = 170\).
Use the identity \((a - b)^2 = (a + b)^2 - 4ab\).
Substitute the values: \((a - b)^2 = 27^2 - 4 \times 170 = 729 - 680 = 49\).
Take the square root: \(a - b = \sqrt{49} = 7\).
As a check, the numbers are 10 and 17, whose sum is 27 and product is 170.
Hence, the positive difference between the two numbers is 7.
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Important Questions from Algebra
In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.
I. x2 – 26x + 165 = 0
II. y2 – 38y + 357 = 0
Factorize the following:
(x 2- 6xy + 9y 2) - 25
If P and Q are the points on the line Joining A(-2, 5) and B(3, 1) such that
AP = PQ = QB, then the mid point of PQ is
If a number and its reciprocal added it becomes 6, then what will be sum of its square and square of its reciprocal?
If 3x + 2y = 15, and xy = 6. Find the value of (3x3/2) + (4y3/9).
