@@ -37,58 +37,59 @@ async function generateContent(
3737
3838 console . log ( response . text ) ;
3939
40+ // Example Response:
41+ // Okay, let's solve the quadratic equation x² + 4x + 4 = 0.
42+ //
43+ // We can solve this equation by factoring, using the quadratic formula,
44+ // or by recognizing it as a perfect square trinomial.
45+ //
46+ // **Method 1: Factoring**
47+ //
48+ // 1. We need two numbers that multiply to the constant term (4)
49+ // and add up to the coefficient of the x term (4).
50+ // 2. The numbers 2 and 2 satisfy these conditions: 2 * 2 = 4 and 2 + 2 = 4.
51+ // 3. So, we can factor the quadratic as:
52+ // (x + 2)(x + 2) = 0
53+ // or
54+ // (x + 2)² = 0
55+ // 4. For the product to be zero, the factor must be zero:
56+ // x + 2 = 0
57+ // 5. Solve for x:
58+ // x = -2
59+ //
60+ // **Method 2: Quadratic Formula**
61+ //
62+ // The quadratic formula for an equation ax² + bx + c = 0 is:
63+ // x = [-b ± sqrt(b² - 4ac)] / (2a)
64+ //
65+ // 1. In our equation x² + 4x + 4 = 0, we have a = 1, b = 4, and c = 4.
66+ // 2. Substitute these values into the formula:
67+ // x = [-4 ± sqrt(4² - 4 * 1 * 4)] / (2 * 1)
68+ // x = [-4 ± sqrt(16 - 16)] / 2
69+ // x = [-4 ± sqrt(0)] / 2
70+ // x = [-4 ± 0] / 2
71+ // x = -4 / 2
72+ // x = -2
73+ //
74+ // **Method 3: Perfect Square Trinomial**
75+ //
76+ // 1. Notice that the expression x² + 4x + 4 fits the pattern of a perfect square trinomial:
77+ // a² + 2ab + b², where a = x and b = 2.
78+ // 2. We can rewrite the equation as:
79+ // (x + 2)² = 0
80+ // 3. Take the square root of both sides:
81+ // x + 2 = 0
82+ // 4. Solve for x:
83+ // x = -2
84+ //
85+ // All methods lead to the same solution.
86+ //
87+ // **Answer:**
88+ // The solution to the equation x² + 4x + 4 = 0 is x = -2.
89+ // This is a repeated root (or a root with multiplicity 2).
90+
4091 return response . text ;
4192}
42- // Example Response:
43- // Okay, let's solve the quadratic equation x² + 4x + 4 = 0.
44- //
45- // We can solve this equation by factoring, using the quadratic formula,
46- // or by recognizing it as a perfect square trinomial.
47- //
48- // **Method 1: Factoring**
49- //
50- // 1. We need two numbers that multiply to the constant term (4)
51- // and add up to the coefficient of the x term (4).
52- // 2. The numbers 2 and 2 satisfy these conditions: 2 * 2 = 4 and 2 + 2 = 4.
53- // 3. So, we can factor the quadratic as:
54- // (x + 2)(x + 2) = 0
55- // or
56- // (x + 2)² = 0
57- // 4. For the product to be zero, the factor must be zero:
58- // x + 2 = 0
59- // 5. Solve for x:
60- // x = -2
61- //
62- // **Method 2: Quadratic Formula**
63- //
64- // The quadratic formula for an equation ax² + bx + c = 0 is:
65- // x = [-b ± sqrt(b² - 4ac)] / (2a)
66- //
67- // 1. In our equation x² + 4x + 4 = 0, we have a = 1, b = 4, and c = 4.
68- // 2. Substitute these values into the formula:
69- // x = [-4 ± sqrt(4² - 4 * 1 * 4)] / (2 * 1)
70- // x = [-4 ± sqrt(16 - 16)] / 2
71- // x = [-4 ± sqrt(0)] / 2
72- // x = [-4 ± 0] / 2
73- // x = -4 / 2
74- // x = -2
75- //
76- // **Method 3: Perfect Square Trinomial**
77- //
78- // 1. Notice that the expression x² + 4x + 4 fits the pattern of a perfect square trinomial:
79- // a² + 2ab + b², where a = x and b = 2.
80- // 2. We can rewrite the equation as:
81- // (x + 2)² = 0
82- // 3. Take the square root of both sides:
83- // x + 2 = 0
84- // 4. Solve for x:
85- // x = -2
86- //
87- // All methods lead to the same solution.
88- //
89- // **Answer:**
90- // The solution to the equation x² + 4x + 4 = 0 is x = -2.
91- // This is a repeated root (or a root with multiplicity 2).
9293
9394// [END googlegenaisdk_thinking_with_txt]
9495
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