Question

if xy = 20, (x-y)=1, then the value
of (x+y) = 9. true or false

please help
it is urgent
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Answer 1

Step-by-step explanation:

Given:xy = 20, (x-y)=1.

To find: The value of (x+y) = 9. State true or false.

Solution:

Step 1 : square (x-y)=1 both sides

$( {x - y)}^{2} = ( {1)}^{2} \\ \\ {x}^{2} - 2xy + {y}^{2} = 1$

Step 2: Add 4xy both sides

${x}^{2} - 2xy + 4xy + {y}^{2} = 1 + 4xy \\ \\ {x}^{2} + 2xy + {y}^{2} = 1 + 4xy$

Step 3: Make whole square in LHS and put value of xy in RHS

$( {x + y)}^{2} = 1 + 4 \times 20 \\ \\ ( {x + y)}^{2} = 1 + 80 \\ \\ ( {x + y)}^{2} = 81$

Step 4: Take square both sides

$x + y = ±9$

Final answer:

Yes, it is true that (x+y)=9.

But another value is also present,(x+y)=-9

(x+y)=±9

Hope it helps you.

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