Question

of 5x + 8y = 10 and xy = 0.25 find 5x-8y​

Answer 1

Answer:

$\sqrt{60}$

Step-by-step explanation:

xy = 0.25  ................(1)

5x + 8y = 10

( 5x + 8y)^2 = 100           ......(squaring both sides )

(5x)^2 + (8y)^2 + 2*5x*8y = 100

(5x)^2 + (8y)^2 + 80xy = 100

(5x)^2 + (8y)^2 + 80(0.25) = 100     .............using (1)

(5x)^2 + (8y)^2 + 20 = 100

(5x)^2 + (8y)^2 = 100-20 = 80  .........................(2)

(5x)^2 + (8y)^2 = (5x - 8y)^2 +(5x)(8y)

80 = (5x - 8y)^2  + 40xy                                ..............................using(2)

80 = (5x - 8y)^2  +  40(0.25)                      ..................................using(1)

80 = (5x - 8y)^2  +  10

80 - 10  = (5x - 8y)^2  

(5x - 8y)^2   = 70

5x-8y = $\sqrt{60}$

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