Question

find the value of 16xy,4xy,6xy,????​

Answer 1

Given points are A(6, 1), B(1, 3) and C(x, 8). We need to find the value of x such that AB = BC.

We know that the distance between the points (x1, y1) and (x2, y2) is

⇒ AB = BC

⇒ AB2 = BC2

⇒ (6 - 1)2 + (1 - 3)2 = (1 - x)2 + (3 - 8)2

⇒ (5)2 + (- 2)2 = (1 - x)2 + (- 5)2

⇒ 25 + 4 = 1 - 2x + x2 + 25

⇒ x2 - 2x - 3 = 0

⇒ x2 - 3x + x - 3 = 0

⇒ x(x - 3) + 1(x - 3) = 0

⇒ (x + 1)(x - 3) = 0

⇒ x + 1 = 0 (or) x - 3 = 0

⇒ x = - 1 (or) x = 3

∴ The values of x are - 1 or 3.

Answer 2

Step-by-step explanation:

x+y=√3 ____i

x-y=√2_____ii

Square (i) & (ii)

x²+y²+2xy=3 __iii , x²+y²-2xy=2 ___iv

Adding above eqs.

2{x²+y²}=5

Subtracting (iii) - (iv)

4xy=1

16xy(x²+y²) can be written as 2*(4xy)*(2(x²+y²))

16xy(x²+y²) = 10.

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