have you studied the equation of parabola and associated quadratic equations ?the sum of two numbers is 64. show that their product has a maximum of 1024.
You don't want to find two numbers whose product is 1024, but to show that the product is never greater than 1024.the sum of two numbers is 64. show that their product has a maximum of 1024.
thank you!!!!For all readers, the graph of
y = ax^2 + bx + c
is a parabola that opens upwards or downwards, and the x-coordinate of the parabola's vertex point is given by
x = -b/(2a)
Hint for remembering: For those who've learned about the Quadratic Formula and its Discriminant, you can remember -b/(2a) as the x-value we get from the Quadratic Formula when the Discriminant is zero.
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thank u!!!For all readers, the graph of
y = ax^2 + bx + c
is a parabola that opens upwards or downwards, and the x-coordinate of the parabola's vertex point is given by
x = -b/(2a)
Hint for remembering: For those who've learned about the Quadratic Formula and its Discriminant, you can remember -b/(2a) as the x-value we get from the Quadratic Formula when the Discriminant is zero.
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yep, don't worry I've figured it just today, thank u!have you studied the equation of parabola and associated quadratic equations ?
thank uuuTo wrap up:
Let the numbers be 'a' & 'b '. Then
a + b = 64 .....so........ b = 64 - a
a * b = a *(64 - a) = -a^2 + 64 * a = P(roduct)
Maximum value of P @ a =- (-64)/[2*(-1)] = 32 ..... & b = 64 - 32 = 32
Check
a + b = 64 ...... & ... a * b = 32 * 32 = 1024..... Checks
thankyouuuIt can be shown that given a sum, that the max product will be half the sum squared.
So the max product will be (.5*64)^2 = 32^2 =1024