From the sum of x² - y² - 1, y² - x² - 1 and 1 - x² - y² subtract - (1 + y²)
Solution:
The given expressions are x² - y² - 1, y² - x² - 1, 1 - x² - y² and - (1 + y²)
We have to find the sum of x² - y² - 1, y² - x² - 1 and 1 - x² - y²
Sum = x² - y² - 1+ (y² - x² - 1) + (1 - x² - y²)
= x² - y² - 1 + y² - x² - 1 + 1 - x² - y²
By combining like terms,
= x² - x² - x² - y² + y² - y² - 1 - 1 + 1
= (1 - 1 - 1)x² + (-1 + 1 - 1)y² + (-1 - 1 + 1)
= (-1)x² + (-1)y² + (-1)
= -x² - y² - 1
Therefore, the sum of x² - y² - 1, y² - x² - 1 and 1 - x² - y² is -x² - y² - 1.
We have to subtract - (1 + y²) from the sum of x² - y² - 1, y² - x² - 1 and 1 - x² - y².
Required expression = -x² - y² - 1 - (- (1 + y²))
= -x² - y² - 1 - (-1 - y²)
= -x² - y² - 1 + 1 + y²
By combining like terms,
= -x² - y² + y² - 1 + 1
= -x²
Therefore, the required expression is -x².
✦ Try This: From the sum of 2x² - 2y² - 1, 3y² - 4x² - 1 and 1 - 2x² - 3y² subtract - (1 + 4y²)
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 12
NCERT Exemplar Class 7 Maths Chapter 10 Problem 70
From the sum of x² - y² - 1, y² - x² - 1 and 1 - x² - y² subtract - (1 + y²)
Summary:
On subtracting -(1 + y²) from the sum of x² - y² - 1, y² - x² - 1 and 1 - x² - y², we get -x²
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