Solve simultaneous linear equations: (i) 9×2 + 12x + 4 – 16y2

Solve simultaneous linear equations:

(i) 9x² + 12x + 4 – 16y²
(ii) x⁴ + 3x² + 4

Solution:

(i) 9x² + 12x + 4 – 16y²
Above terms can be written as,
(3x)² + (2 × 3x × 2) + 2² – 16y²
Then, (3x + 2)² – (4y)²
(3x + 2 + 4y) (3x + 2 – 4y)
(ii) x⁴ + 3x² + 4
x⁴ + 3x² + 4
Above terms can be written as,
(x²)² + 3(x²) + 4
(x²)² + (2)² + 4x² – x²
(x² + 2)² – (x²)
We know that, (a² – b²) = (a + b) (a – b)
(x² + 2 + x) (x² + 2 – x)
(x² + x + 2) (x² – x + 2)

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