Question
Download Solution PDFIf x + y = 8, product of x and y is 15, then the value of x4 + y4 is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
x + y = 8
x × y = 15
Concept Used:
(a + b)2 = a2 + b2 + 2ab
Calculation:
We know,
⇒ (x + y)2 = x2 + y2 + 2xy
Putting the values,
⇒ 82 = x2 + y2 + 2 × 15
⇒ x2 + y2 = 64 – 30 = 34
⇒ x2 + y2 = 34
Squaring both sides, we get
⇒ (x2 + y2)2 = (34)2
⇒ x4 + y4 + 2x2y2 = 1156
⇒ x4 + y4 + 2 × (15)2 = 1156
⇒ x4 + y4 = 1156 – 2 × 225 = 1156 – 450 = 706
Hence, the required value of x4 + y4 is 706.
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