x + y = 9 and xy = 14 find x^2 - y^2
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Answered by
4
x + y = 14
Square on both sides,
x² + y² + 2xy = 196
x² + y² = 196 - 2(14)
x² + y² = 168
Remove 2xy from both sides,
x² + y² - 2xy = 168 - 2(14)
(x - y)² = 140
x - y = √140
Hence,
x² - y²
=> (x + y) (x - y)
=> (9)(√140)
=> 9√(2×2×35)
=> 18√35
Square on both sides,
x² + y² + 2xy = 196
x² + y² = 196 - 2(14)
x² + y² = 168
Remove 2xy from both sides,
x² + y² - 2xy = 168 - 2(14)
(x - y)² = 140
x - y = √140
Hence,
x² - y²
=> (x + y) (x - y)
=> (9)(√140)
=> 9√(2×2×35)
=> 18√35
Answered by
2
x + ʏ = 14
sϙᴜᴀʀᴇ ᴏɴ ʙᴏᴛʜ sɪᴅᴇs,
x² + ʏ² + 2xʏ = 196
x² + ʏ² = 196 - 2(14)
x² + ʏ² = 168
ʀᴇᴍᴏᴠᴇ 2xʏ ғʀᴏᴍ ʙᴏᴛʜ sɪᴅᴇs,
x² + ʏ² - 2xʏ = 168 - 2(14)
(x - ʏ)² = 140
x - ʏ = √140
ʜᴇɴᴄᴇ,
x² - ʏ²
=> (x + ʏ) (x - ʏ)
=> (9)(√140)
=> 9√(2×2×35)
=> 18√35
sϙᴜᴀʀᴇ ᴏɴ ʙᴏᴛʜ sɪᴅᴇs,
x² + ʏ² + 2xʏ = 196
x² + ʏ² = 196 - 2(14)
x² + ʏ² = 168
ʀᴇᴍᴏᴠᴇ 2xʏ ғʀᴏᴍ ʙᴏᴛʜ sɪᴅᴇs,
x² + ʏ² - 2xʏ = 168 - 2(14)
(x - ʏ)² = 140
x - ʏ = √140
ʜᴇɴᴄᴇ,
x² - ʏ²
=> (x + ʏ) (x - ʏ)
=> (9)(√140)
=> 9√(2×2×35)
=> 18√35
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