Solve: (3x - 5)^2 + (3x + 5)^2 = (18x + 10) (x - 2)

MCQ

Solve: $(3x - 5)^2 + (3x + 5)^2 = (18x + 10) (x - 2)$

✓
$\frac{-35}{13}$
B
$\frac{-25}{13}$
C
$\frac{-15}{13}$
D
$\frac{-45}{13}$

✓

Answer

Correct option: A.

$\frac{-35}{13}$

We will solve the given expression
$(3x - 5)^2 + (3x + 5)^2 =(18x + 10) (x - 2)$ as shown below:
$(3x - 5)^2 + (3x + 5)^2 = (18x + 10)(x - 2)$
$\Rightarrow [(3x)^2 + (5)^2 - (2 \times 3x \times 5)] + [(3x)^2 + (5)^2 + (2 \times 3x \times 5)] = 18x (x - 2) + 10(x - 2)$
$\therefore (a + b)^2 = a^2 + b^2 + 2ab, (a - b)^2 = a^2 + b^2 - 2ab)$
$\Rightarrow 9x^2 + 25 - 30x + 9x^2 + 25 + 30x = 18x^2 - 36x + 10x - 20$
$\Rightarrow 18x^2 + 50 =18x^2 - 26x - 20$
$\Rightarrow 18x^2 + 50 - 18x^2 + 26x + 20 = 0$
$\Rightarrow 26x + 70 = 0$
$\Rightarrow 26x = -70$
$\Rightarrow \text{x}=-\frac{70}{26}$
$\Rightarrow\text{x}=-\frac{35}{13}$
Hence, $\text{x}=-\frac{35}{13}$

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