Maths-
General
Easy
Question
If x2=16 and y2=4, find the greatest possible value of (x-y)2
Hint:
In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
an = a × a × ... × a n times.
The correct answer is: Greatest possible value of (x-y)2 is 36.
Step-by-step solution:-
x2=16
∴ x = +/- 4 …................................... (Taking square root both the sides) …...................................... (Equation i)
y2=4
∴ y = +/- 2 …................................... (Taking square root both the sides) …...................................... (Equation ii)
∴ possible combinations of x & y values are-
(4,2); (-4,-2); (-4,2); (4,-2)
Substituting each of these values in the required expression, we get-
a. (4,2)
(x-y)2 = (4-2)2 = 22 = 4
b. (-4,-2)
(x-y)2 = [(-4-(-2)]2 = (-4+2)2 = (-2)2 = 4
c. (-4,2)
(x-y)2 = (-4-2)2 = -62 = 36
d. (4,-2)
(x-y)2 = [(4-(-2)]2 = (4+2)2 = 62 = 36
Final Answer:-
∴ Greatest possible value of (x-y)2 is 36.
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