यदि दो पूर्णांकों के वर्गमूल का योग रूट 18 प्लस 8 रूट 5 है तो पूर्णांकों के वर्गों का योग क्या है
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Given : दो पूर्णांकों के वर्गमूल का योग √18 + 8√5 है
To Find : पूर्णांकों के वर्गों का योग
Solution:
दो पूर्णांक = a , b
√a + √b = √18 + 8√5
=> √a + √b = 3√2 + 8√5
Squaring both sides
=> a + b + 2√ab = 18 + 320 + 48√10
=> a + b + 2√ab = 338 + 48√10
=> a + b = 338
2√ab = 48√10
=> √ab = 24√10
=> ab = 5760
a + b = 338
Squaring both sides
=> a² + b² + 2ab = 1,14,244
=> a² + b² + 2(5760) = 1,14,244
=> a² + b² = 1,02,724
पूर्णांकों के वर्गों का योग = 1,02,724
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