Ask Question
17 April, 04:43

Use the identity (x^2+y^2) ^2 = (x^2-y^2) ^2 + (2xy) ^2 to determine the sum of the squares of two numbers if the difference of the squares of the numbers is 5 and the product of the numbers is 6.

0
Answers (1)
  1. 17 April, 05:26
    0
    Step-by-step explanation:

    (x^2+y^2) ^2 = (x^2) ^2+2x^2y^2 + (y^2) ^2

    Adding and substracting 2x^2y^2

    We get

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

    And we know a^2-2ab+b^2 = (a-b) ^2

    So we identify (x^2) ^2 as a^2, (y^2) ^2 as b^2 and - 2x^2y^2 as - 2ab. So we can rewrite (x^2+y^2) ^2 = (x^2 - y^2) ^2 + 2x^2y^2 + 2x^2y^2 = (x^2 - y^2) ^2+4x^2y^2 = (x^2 - y^2) ^2+2^2x^2y^2

    Moreever we know (a·b·c) ^2=a^2·b^2·c^2 than means 2^2x^2y^2 = (2x·y) ^2

    And (x^2+y^2) ^2 = (x^2 - y^2) ^2 + (2x·y) ^2
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Use the identity (x^2+y^2) ^2 = (x^2-y^2) ^2 + (2xy) ^2 to determine the sum of the squares of two numbers if the difference of the squares ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers