If 16a4 + 36a2b2 + 81b4 = 91 and 4a2 + 9b2 – 6ab = 13, then what is the value of 3ab?
If 16a4 + 36a2b2 + 81b4 = 91 and 4a2 + 9b2 – 6ab = 13, then what is the value of 3ab? Correct Answer –3/2
16a4 + 36a2b2 + 81b4 = 91
⇒ (4a2)2 + 4a2 × 9b2 + (9b2)2 = 91
⇒ Adding 4a2 × 9b2 to make (a + b)2
⇒ (4a2)2 + 2(4a2 × 9b2) + (9b2)2 = 91 + 4a2 × 9b2
⇒ (4a2 + 9b2)2 = 91 + 36a2b2 ----(1)
Now, 4a2 + 9b2 – 6ab = 13
⇒ 4a2 + 9b2 = 13 + 6ab ----(2)
Putting equation 2 in equation 1
⇒ (13 + 6ab)2 = 91 + 36a2b2
⇒ 169 + 36 a2b2 + 156ab = 91 + 36 a2b2
⇒ 156ab = - 78
⇒ ab = - ½
⇒ 3ab = - 3/2
মোঃ আরিফুল ইসলাম
Feb 20, 2025