Question

if 2x-5y=8 and xy=4, Find the value of 4x²+25y².​

Answer 1

Step-by-step explanation:

(2x-5y) ^2= 4x^2+25y^2-20xy

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

=> 4x^2+25^2-20xy= 64

=> 4x^2+25y^2= 64+20xy

now

64+20xy= 64+ 20*4(as xy= 4)

= 64+80

= 144

So

4x^2+25y^2= 144

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Answer 2

Given,

2x-5y=8 and xy=4

To find,

The value of 4x²+25y².

Solution,

The value of 4x²+25y² will be 144.

We can easily solve this problem by following the given steps.

According to the question,

We have: 2x-5y=8

Now, square on both sides,

(2x-5y)² = (8)²

Using the identity: (a-b)² = a²+b²-2ab

(2x)²+(5y)²-2(2x)(5y) = 64

4x²+25y²-20xy = 64

Now, putting the value of xy to be 4 in this expression:

4x²+25y²-20(4) = 64

4x²+25y²-80 = 64

Moving 80 from the left-hand side to the right-hand side will result in the change of the sign from minus to plus:

4x²+25y² = (64+80)

4x²+25y² = 144

Hence, the value of 4x²+25y² is 144.