Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
201 views
in Algebra by (237k points)
closed by
x and y are positive real numbers. If x4 + y4 + x2y2 = 576 and xy = 7, then what is the value of (x - y)?
1. 25
2. 11
3. 9
4. 16

1 Answer

0 votes
by (239k points)
selected by
 
Best answer
Correct Answer - Option 2 : 11

Given:

x4 + y4 + x2y2 = 576 and xy = 7

Formula used:

(x + y)2 = x2 + y2 + 2xy

Calculations:

x4 + y4 + x2y2 = 576

Adding x2yin both side of the equation. 

⇒ (x2 + y2)2 – x2y2 = 576

⇒ (x2 + y2)2 – (7)2 = 576

⇒ (x2 + y2)2 – 49 = 576

⇒ (x2 + y2)2 = 576 + 49 = 625

⇒ (x2 + y2) = 25

Thus x2 + y2 - 2xy = 25 - 2 × 7 = 11

⇒ (x - y)2 = 11

∴  The value of (x - y)2 is 11.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...