The difference between two positive numbers is 7 and the difference between thes cubes is 805. If 'A' represents their product and 'B' represents the sum of their squares,
find the value of 'A-B'.​

The  difference between two positive numbers is 7 and the difference between these  cubes is 805. If 'A' represents their product and 'B' represents the sum of their squares,

So,

Let the number be n and m

A = n × m = nm

B = n² + m² = (n + m)²

Now

n³ - m³ = 805

(n - m) (n² + m² + nm) = 805

Since difference is 7

7 × n² + m² + nm = 805

n² + m² + nm = 805/7

n² + m² + nm = 115

(n² + n) + (m² + m) = 115

A + B = 115

Now

On squaring the first eq.

(n - m)² = (7)²

(n - m)² = 49

B - 2A = 49

Now

A + B - B + 2A = 115 - 49

A + 2A = 66

3A = 66

A = 66/3

A = 22

By using 2

B - 2(22) = 49

B - 44 = 49

B = 49 + 44

B = 93

A - B = 22 - 93 = -71

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.  

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,