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Given that (8 - ✓x)(5 + ✓x) = y√x + 21 where x is a prime number and y is an integer,

find the value of x and the value of y.

Show each stage of your working clearly.​
thank you:⁠-⁠D

User PC Jones
by
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1 Answer

2 votes

Answer:

  • x = 19
  • y = 3

Explanation:

You want the values of x and y that make (8-√x)(5+√x) ≡ 21 +y√x.

Solution

The product is ...

(8-√x)(5+√x) = 8·5 -5√x +8√x -(√x)²

Comparing this to the right-side expression, we see ...

40-x +3√x = 21 +y√x

Matching integer parts, we have ...

40 -x = 21

40 -21 = x = 19

Matching radical parts, we have ...

3√x = y√x

3 = y

The values of x and y are 19 and 3, respectively.

(8 -√19)(5 +√19) = 21 +3√19

Given that (8 - ✓x)(5 + ✓x) = y√x + 21 where x is a prime number and y is an integer-example-1
User Aaron Butacov
by
4.7k points
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